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A Caputo et al arXiv:2001.03620 [gr-qc] (D3.1)

Gravitational-wave detection and parameter estimation for accreting black-hole binaries and their electromagnetic counterpart
We study the impact of gas accretion on the orbital evolution of black-hole binaries initially at large separation in the band of the planned Laser Interferometer Space Antenna (LISA). We focus on two sources: (i) stellar-origin black-hole binaries (SOBHBs) that can migrate from the LISA band to the band of ground-based gravitational-wave observatories within weeks/months; and (ii) intermediate-mass black-hole binaries (IMBHBs) in the LISA band only. Because of the large number of observable gravitational-wave cycles, the phase evolution of these systems needs to be modeled to great accuracy to avoid biasing the estimation of the source parameters. Accretion affects the gravitational-wave phase at negative (-4) post-Newtonian order, and is therefore dominant for binaries at large separations. If accretion takes place at the Eddington or at super-Eddington rate, it will leave a detectable imprint on the dynamics of SOBHBs. In optimistic astrophysical scenarios, a multiwavelength strategy with LISA and a ground-based interferometer can detect about 10 (a few) SOBHB events for which the accretion rate can be measured at 50% (10%) level. In all cases the sky position can be identified within much less than 0.4 deg² uncertainty. Likewise, accretion at ≳10% (≳100%) of the Eddington rate can be measured in IMBHBs up to redshift z ≈ 0.1 (z ≈ 0.5), and the position of these sources can be identified within less than 0.01 deg² uncertainty. Altogether, a detection of SOBHBs or IMBHBs would allow for targeted searches of electromagnetic counterparts to black-hole mergers in gas-rich environments with future X-ray detectors (such as Athena) and radio observatories (such as SKA).
Deliverable D3.1 (Compact binary waveform)

V Cardoso, F Duque, T Ikeda arXiv:2001.01729 [gr-qc] (D1.1)

P V P Cunha, N A Eiró, C A R Herdeiro, J P S Lemos arXiv:1912.08833 [gr-qc] (D2.3)

Lensing and shadow of a black hole surrounded by a heavy accretion disk
We consider a static, axially symmetric spacetime describing the superposition of a Schwarzschild black hole (BH) with a thin and heavy accretion disk. The BH-disk configuration is a solution of the Einstein field equations within the Weyl class. The disk is sourced by a distributional energy-momentum tensor and it is located at the equatorial plane. It can be interpreted as two streams of counter-rotating particles, yielding a total vanishing angular momentum. The phenomenology of the composed system depends on two parameters: the fraction of the total mass in the disk, m, and the location of the inner edge of the disk, a. We start by determining the sub-region of the space of parameters wherein the solution is physical, by requiring the velocity of the disk particles to be sub-luminal and real. Then, we study the null geodesic flow by performing backwards ray-tracing under two scenarios. In the first scenario the composed system is illuminated by the disk and in the second scenario the composed system is illuminated by a far-away celestial sphere. Both cases show that, as m grows, the shadow becomes more prolate. Additionally, the first scenario makes clear that as m grows, for fixed a, the geometrically thin disk appears optically enlarged, i.e., thicker, when observed from the equatorial plane. This is to due to light rays that are bent towards the disk, when backwards ray traced. In the second scenario, these light rays can cross the disk (which is assumed to be transparent) and may oscillate up to a few times before reaching the far away celestial sphere. Consequently, an almost equatorial observer sees different patches of the sky near the equatorial plane, as a chaotic "mirage". As m → 0 one recovers the standard test, i.e., negligible mass, disk appearance.
Deliverable D2.3 (Shadows of single black holes)

L G Collodel, B Kleihaus, J Kunz, E Berti arXiv:1912.05382 [gr-qc] (D3.3)

D Astefanesei, J L Blázquez-Salcedo, C Herdeiro, E Radu, N Sanchis-Gual arXiv:1912.02192 [gr-qc] (D3.3)

Dynamically and thermodynamically stable black holes in Einstein-Maxwell-dilaton gravity
We consider Einstein-Maxwell-dilaton gravity with the non-minimal exponential coupling between the dilaton and the Maxwell field emerging from low energy heterotic string theory. The dilaton is endowed with a potential that originates from an electromagnetic Fayet-Iliopoulos (FI) term in 𝒩 = 2 extended supergravity in four spacetime dimensions. For the case we are interested in, this potential introduces a single parameter α. When α → 0, the static black holes (BHs) of the model are the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) solutions. When α → ∞, the BHs become the standard Reissner-Nordström (RN) solutions of electrovacuum General Relativity. The BH solutions for finite non-zero 𝛼 interpolate between these two families. In this case, the dilaton potential regularizes the extremal limit of the GMGHS solution yielding a set of zero temperature BHs with a near horizon AdS₂ × S₂. geometry. We show that, in the neighborhood of these extremal solutions, there is a subset of BHs that are dynamically and thermodynamically stable, all of which have charge to mass ratio larger than unity. By dynamical stability we mean that no growing quasi-normal modes are found; thus they are stable against linear perturbations (spherical and non-spherical). Moreover, non-linear numerical evolutions lend support to their non-linear stability. By thermodynamical stability we mean the BHs are stable both in the canonical and grand-canonical ensemble. In particular, both the specific heat at constant charge and the isothermal permittivity are positive. This is not possible for RN and GMGHS BHs. We discuss the different thermodynamical phases for the BHs in this model and comment on what may allow the existence of both dynamically and thermodynamically stable BHs.
Deliverable D3.3 (Smoking Guns)

M Wang, C Herdeiro, J Jing arXiv:1910.14305 [gr-qc] Phys.Rev.D 100 (2019) 124062 (D2.2)

A Maselli, P Pani, L Gualtieri, E Berti arXiv:1910.12893 [gr-qc] (D3.3)

C A R Herdeiro, J M S Oliveira, E Radu arXiv:1910.11021 [gr-qc] Eur.Phys.J. C 80 (2020) 23 (D2.1), (D2.2)

V Cardoso, L Gualtieri, C J Moore arXiv:1910.09557 [gr-qc] Phys.Rev.D 100 (2019) 124037 (D3.2), (D4.3)

J Y Widdicombe, T Helfer, E A Lim arXiv:1910.01950 [gr-qc] JCAP 2001 (2020) 027 (D1.3), (D4.2)

U Sperhake, R Rosca-Mead, D Gerosa, E Berti arXiv:1910.01598 [gr-qc] Phys.Rev.D 101 (2020) 024044 (D3.1)

C A R Herdeiro, J M S Oliveira arXiv:1909.08915 [gr-qc] Phys.Lett.B 800 (2020) 135076 (D1.2)

P V P Cunha, C A R Herdeiro, E Radu arXiv:1909.08039 [gr-qc] Universe 5 (2019) 220 (D1.1), (D2.3)

V Cardoso, A Maselli arXiv:1909.05870 [astro-ph] (D1.3)

U Sperhake, W Cook, D Wang arXiv:1909.02997 [gr-qc] Phys.Rev.D 100 (2019) 104046 (D4.2)

P G S Fernandes, C A R Herdeiro, A M Pombo, E Radu, N Sanchis-Gual arXiv:1908.00037 [hep-th] Phys.Rev.D 100 (2019) 084045 (D2.1)

M Bastero-Gil, A Berera, R O Ramos, J G Rosa arXiv:1907.13410 [hep-ph] (D1.1), (D1.4)

N Sanchis-Gual, F Di Giovanni, M Zilhão, C Herdeiro, P Cerdá-Durán, J A Font, E Radu arXiv:1907.12565 [gr-qc] Phys.Rev.Lett. 123 (2019) 221101 (D1.2)

E Barausse arXiv:1907.05958 [gr-qc] Phys.Rev.D 100 (2019) 084053 (D3.1), (D3.2)

N Tamanini, A Klein, C Bonvin, E Barausse, C Caprini arXiv:1907.02018 [astro-ph] (D3.1), (D3.2)

The peculiar acceleration of stellar-origin black hole binaries: measurement and biases with LISA
We investigate the ability of the Laser Interferometer Space Antenna (LISA) to measure the center of mass acceleration of stellar-origin black hole binaries emitting gravitational waves. Our analysis is based on the idea that the acceleration of the center of mass induces a time variation in the redshift of the gravitational wave, which in turn modifies its waveform. We confirm that while the cosmological acceleration is too small to leave a detectable imprint on the gravitational waveforms observable by LISA, larger peculiar accelerations may be measurable for sufficiently long lived sources. We focus on stellar mass black hole binaries, which will be detectable at low frequencies by LISA and near coalescence by ground based detectors. These sources may have large peculiar accelerations, for instance, if they form in nuclear star clusters or in AGN accretion disks. If that is the case, we find that in an astrophysical population calibrated to the LIGO-Virgo observed merger rate, LISA will be able to measure the peculiar acceleration of a small but significant fraction of the events if the mission lifetime is extended beyond the nominal duration of 4 years. In this scenario LISA will be able to assess whether black hole binaries form close to galactic centers, particularly in AGN disks, and will thus help discriminate between different formation mechanisms. Although for a nominal 4 years LISA mission the peculiar acceleration effect cannot be measured, a consistent fraction of events may be biased by strong peculiar accelerations which, if present, may imprint large systematic errors on some waveform parameters. In particular, estimates of the luminosity distance could be strongly biased and consequently induce large systematic errors on LISA measurements of the Hubble constant with stellar mass black hole binaries.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)

V Cardoso, A del Río, M Kimura arXiv:1907.01561 [gr-qc] Phys.Rev.D 100 (2019) 084046 (D1.1), (D3.3)

J G Rosa, L B Ventura arXiv:1906.11835 [hep-ph] Phys.Lett.B 798 (2019) 134984 (D1.1), (D1.4)

V Cardoso, R Vicente arXiv:1906.10140 [gr-qc] Phys.Rev.D 100 (2019) 084001 (D2.3)

C Herdeiro, I Perapechka, E Radu, Ya Shnir arXiv:1906.05386 [gr-qc] Phys.Lett.B 797 (2019) 134845 (D1.2)

Asymptotically flat spinning scalar, Dirac and Proca stars
Einstein's gravity minimally coupled to free, massive, classical fundamental fields admits particle-like solutions. These are asymptotically flat, everywhere non-singular configurations that realise Wheeler's concept of a geon: a localised lump of self-gravitating energy whose existence is anchored on the non-linearities of general relativity, trivialising in the flat spacetime limit. In arXiv:1708.05674 the key properties for the existence of these solutions (also referred to as stars or self-gravitating solitons) were discussed - which include a harmonic time dependence in the matter field -, and a comparative analysis of the stars arising in the Einstein-Klein-Gordon, Einstein-Dirac and Einstein-Proca models was performed, for the particular case of static, spherically symmetric spacetimes. In the present work we generalise this analysis for spinning solutions. In particular, the spinning Einstein-Dirac stars are reported here for the first time. Our analysis shows that the high degree of universality observed in the spherical case remains when angular momentum is allowed. Thus, as classical field theory solutions, these self-gravitating solitons are rather insensitive to the fundamental fermionic or bosonic nature of the corresponding field, displaying similar features. We describe some physical properties and, in particular, we observe that the angular momentum of the spinning stars satisfies the quantisation condition J = πmN, for all models, where N is the particle number and m is an integer for the bosonic fields and a half-integer for the Dirac field. The way in which this quantisation condition arises, however, is more subtle for the non-zero spin fields.
Deliverable D1.2 (Structure of stars with dark cores)

R McManus, E Berti, C F B Macedo, M Kimura, A Maselli, V Cardoso arXiv:1906.05155 [gr-qc] Phys.Rev.D 100 (2019) 044061 (D3.3)

V Baibhav et al arXiv:1906.04197 [gr-qc] Phys.Rev.D 100 (2019) 064060 (D3.2)

E Belgacem et al arXiv:1906.01593 [astro-ph] JCAP 1907 (2019) 024 (D3.2)

Testing modified gravity at cosmological distances with LISA standard sirens
Modifications of General Relativity leave their imprint both on the cosmic expansion history through a non-trivial dark energy equation of state, and on the evolution of cosmological perturbations in the scalar and in the tensor sectors. In particular, the modification in the tensor sector gives rise to a notion of gravitational-wave (GW) luminosity distance, different from the standard electromagnetic luminosity distance, that can be studied with standard sirens at GW detectors such as LISA or third-generation ground based experiments. We discuss the predictions for modified GW propagation from some of the best studied theories of modified gravity, such as Horndeski or the more general degenerate higher order scalar-tensor (DHOST) theories, non-local infrared modifications of gravity, bigravity theories and the corresponding phenomenon of GW oscillation, as well as theories with extra or varying dimensions. We show that modified GW propagation is a completely generic phenomenon in modified gravity. We then use a simple parametrization of the effect in terms of two parameters (Ξ0,n), that is shown to fit well the results from a large class of models, to study the prospects of observing modified GW propagation using supermassive black hole binaries as standard sirens with LISA . We construct mock source catalogs and perform detailed Markov Chain Monte Carlo studies of the likelihood obtained from LISA standard sirens alone, as well as by combining them with CMB, BAO and SNe data to reduce the degeneracies between cosmological parameters. We find that the combination of LISA with the other cosmological datasets allows one to measure the parameter Ξ0 that characterizes modified GW propagation to the percent level accuracy, sufficient to test several modified gravity theories. LISA standard sirens can also improve constraints on GW oscillations induced by extra field content by about three orders of magnitude relative to the current capability of ground detectors. We also update the forecasts on the accuracy on H0 and on the dark-energy equation of state using more recent estimates for the LISA sensitivity.
Deliverable D3.2 (Astrophysical Observables)

Y Bouffanais, M Mapelli, D Gerosa, U N Di Carlo, N Gicobbo, E Berti, V Baibhav arXiv:1905.11054 [astro-ph] Astrophys.J. 886 (2019) 25 (D3.2)

S Tanay, A Klein, E Berti, A Nishizawa arXiv:1905.08811 [gr-qc] Phys.Rev.D 100 (2019) 064006 (D3.1)

D Astefanesei, C Herdeiro, A Pombo, E Radu arXiv:1905.08304 [hep-th] JHEP 1910 (2019) 078 (D2.2)

R Vicente, V Cardoso, M Zilhão arXiv:1905.06353 [astro-ph] MNRAS 489 (2019) 5424 (D3.2)

A Maselli, G Pappas, P Pani, L Gualtieri, S Motta, V Ferrari, L Stella arXiv:1905.05616 [astro-ph] (D3.2)

L Bernard, V Cardoso, T Ikeda, M Zilhão arXiv:1905.05204 [gr-qc] Phys.Rev.D 100 (2019) 044002 (D3.1)

P V P Cunha, C A R Herdeiro, E Radu arXiv:1904.09997 [gr-qc] Phys.Rev.Lett. 123 (2019) 011101 (D2.1), (D3.3)

Spontaneously scalarised Kerr black holes in extended scalar-tensor-Gauss-Bonnet gravity
We construct asymptotically flat, spinning, regular on and outside an event horizon, scalarised black holes (SBHs) in extended scalar-tensor-Gauss-Bonnet models. They reduce to Kerr BHs when the scalar field vanishes. For an illustrative choice of non-minimal coupling, we scan the domain of existence. For each value of spin, SBHs exist in an interval between two critical masses, with the lowest one vanishing in the static limit. Non-uniqueness with Kerr BHs of equal global charges is observed; the SBHs are entropically favoured. This suggests SBHs form dynamically from the spontaneous scalarisation of Kerr BHs, which are prone to a scalar-triggered tachyonic instability, below the largest critical mass. Phenomenologically, the introduction of BH spin damps the maximal observable difference between comparable scalarised and vacuum BHs. In the static limit, (perturbatively stable) SBHs can store over 20% of the spacetime energy outside the event horizon; in comparison with Schwarzschild BHs, their geodesic frequency at the ISCO can differ by a factor of 2.5 and deviations in the shadow areal radius may top 40%. As the BH spin grows, low mass SBHs are excluded, and the maximal relative differences decrease, becoming of order ∼ few % for dimensionless spin j ≳ 0.5. This reveals a spin selection effect: non-GR effects are only significant for low spin. We discuss if and how the recently measured shadow size of the M87 supermassive BH, constrains the length scale of the Gauss-Bonnet coupling.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D3.3 (Smoking Guns)

V Cardoso, P Pani arXiv:1904.05363 [gr-qc] Living Rev.Rel. 22 (2019) 4 (D1.2)

V Cardoso, T Igata, A Ishibashi, K Ueda arXiv:1904.05109 [gr-qc] Phys.Rev.D 100 (2019) 044013 (D4.3)

E Berti, R Brito, C F B Macedo, G Raposo, J L Rosa arXiv:1904.03131 [gr-qc] Phys.Rev.D 99 (2019) 104039 (D1.1), (D1.3)

R Rosca-Mead, C J Moore, M Agathos, U Sperhake arXiv:1903.09704 [gr-qc] Class.Quant.Grav.36 (2019) 134003 (D3.3)

C F B Macedo, J Sakstein, E Berti, L Gualtieri, H O Silva, T P Sotiriou arXiv:1903.06784 [gr-qc] Phys.Rev.D 99 (2019) 104041 (D2.1)

E Berti et al arXiv:1903.02781 [astro-ph] (D3.3)

J F M Delgado, C A R Herdeiro, E Radu arXiv:1903.01488 [gr-qc] Phys.Lett.B 792 (2019) 436-444 (D2.1)

V Cardoso, V F Foit, M Kleban arXiv:1902.10164 [hep-th] JCAP 2019 (2019) 006 (D3.3)

C Shi et al arXiv:1902.08922 [gr-qc] Phys.Rev.D 100 (2019) 044036 (D3.3)

C A R Herdeiro, J M S Oliveira arXiv:1902.07721 [gr-qc] Class.Quant.Grav. 36 (2019) 105015 (D2.2)

C A R Herdeiro, N M Santos arXiv:1902.06748 [gr-qc] Phys.Rev.D 99 (2019) 084029 (D1.2)

O Sarbach, E Barausse, J A Preciado-López arXiv:1902.05130 [gr-qc] Class.Quant.Grav. 36 (2019) 165007 (D3.3)

P G S Fernandes, C A R Herdeiro, A M Pombo, E Radu, N Sanchis-Gual arXiv:1902.05079 [gr-qc] Class.Quant.Grav. 36 (2019) 134002 (D2.2)

Spontaneous Scalarisation of Charged Black Holes: Coupling Dependence and Dynamical Features
Spontaneous scalarisation of electrically charged, asymptotically flat Reissner-Nordström black holes (BHs) has been recently demonstrated to occur in Einstein-Maxwell-Scalar (EMS) models. EMS BH scalarisation presents a technical simplification over the BH scalarisation that has been conjectured to occur in extended Scalar-Tensor Gauss-Bonnet (eSTGB) models. It is then natural to ask: 1) how universal are the conclusions extracted from the EMS model? And 2) how much do these conclusions depend on the choice of the non-minimal coupling function? Here we perform a comparative analysis of different forms for the coupling function including: exponential, hyperbolic, power-law and a rational function (fraction) couplings. In all of them we obtain and study the domain of existence of fundamental, spherically symmetric, scalarised BHs and compute, in particular, their entropy. The latter shows that scalarised EMS BHs are always entropically preferred over the RN BHs with the same total charge to mass ratio q. This contrasts with the case of eSTGB, where for the same power-law coupling the spherical, fundamental scalarised BHs are not entropically preferred over Schwarzschild. Also, while the scalarised solutions in the EMS model for the exponential, hyperbolic and power-law coupling are very similar, the rational function coupling leads to a transition in the domain of existence. Furthermore, fully non-linear dynamical evolutions of unstable RN BHs with different values ofq are presented. These show: 1) for sufficiently small q, scalarised solutions with (approximately) the same q form dynamically; 2) for large q, spontaneous scalarisation visibly decreases q; thus evolutions are non-conservative; 3) despite the existence of non-spherical, static scalarised solutions, the evolution of unstable RN BHs under non-spherical perturbations leads to a spherical scalarised BH.
Deliverable D2.2 (Black holes with gauge fields)

H-T Wang et al arXiv:1902.04423 [astro-ph] Phys.Rev.D 100 (2019) 043003 (D3.2)

C A R Herdeiro, E Radu arXiv:1901.02953 [gr-qc] Phys.Rev.D 99 (2019) 084039 (D2.1)

L Annulli, V Cardoso, L Gualtieri arXiv:1901.02461 [gr-qc] Phys.Rev.D 99 (2019) 044038 (D1.4), (D3.3)

M Bastero-Gil, A Berera, R Hernández-Jiménez, J G Rosa arXiv:1812.07296 [hep-ph] Phys.Rev.D 99 (2019) 103520 (D1.1), (D1.4)

H O Silva, C F B Macedo, T P Sotiriou, L Gualtieri, J Sakstein, E Berti arXiv:1812.05590 [gr-qc] Phys.Rev.D 99 (2019) 064011 (D3.3)

M Bonetti, A Sesana, F Haardt, E Brausse, M Colpi arXiv:1812.01011 [astro-ph] Phys.Rev.D 97 (2018) 084020 (D3.2)

Post-Newtonian Evolution of Massive Black Hole Triplets in Galactic Nuclei: IV. Implications for LISA
Coalescing massive black hole binaries (MBHBs) of 10^{4 - 7} M_⊙, forming in the aftermath of galaxy mergers, are primary targets of the space mission LISA, the Laser Interferometer Space Antenna. An assessment of LISA detection prospects requires an estimate of the abundance and properties of MBHBs that form and evolve during the assembly of cosmic structures. To this aim, we employ a semi-analytic model to follow the co-evolution of MBHBs within their host galaxies. We identify three major evolutionary channels driving the binaries to coalescence: two standard paths along which the binary evolution is driven by interactions with the stellar and/or gaseous environment, and a novel channel where MBHB coalescence occurs during the interaction with a third black hole. For each channel, we follow the orbital evolution of MBHBs with physically motivated models that include a self-consistent treatment of the orbital eccentricity. We find that LISA will detect between ≈25 and ≈75 events per year depending on the seed model. We show that triple-induced coalescences can range from a few detected events up to ∼30% of the total detected mergers. Moreover, even if the standard gas/stars-driven evolutionary channels should fail and MBHBs were to stall, triple interactions would still occur as a result of the hierarchical nature of galaxy formation, resulting in about ≈10 to ≈20 LISA detections per year. Remarkably, triple interactions among the black holes can produce coalescing binaries with large eccentricities (≳ 0.9) upon entrance into the LISA band. This eccentricity will remain significant (∼0.1) also at merger, requiring suitable templates for parameter estimation.
Deliverable D3.2 (Astrophysical observables)

C Herdeiro, I Perapechka, E Radu, Y Shnir arXiv:1811.11799 [gr-qc] JHEP 1902 (2019) 111 (D2.1)

A Gimeno-Soler, J A Font, C Herdeiro, E Radu arXiv:1811.11492 [gr-qc] Phys.Rev.D 99 (2019) 043002 (D2.1)

Magnetized accretion disks around Kerr black holes with scalar hair: Constant angular momentum disks
Testing the true nature of black holes—the no-hair hypothesis—will become increasingly more precise in the next few years as new observational data is collected in both the gravitational-wave channel and the electromagnetic channel. In this paper we consider numerically generated spacetimes of Kerr black holes with synchronized scalar hair and build stationary models of magnetized thick disks (or tori) around them. Our approach assumes that the disks are not self-gravitating, they obey a polytropic equation of state, the distribution of their specific angular momentum is constant, and they are marginally stable, i.e., the disks completely fill their Roche lobe. Moreover, contrary to existing approaches in the literature, our models are thermodynamically relativist, as the specific enthalpy of the fluid can adopt values significantly larger than unity. We study the dependence of the morphology and properties of the accretion tori on the type of black hole considered, from purely Kerr black holes with varying degrees of spin parameter, namely from a Schwarzschild black hole to a nearly extremal Kerr case, to Kerr black holes with scalar hair with different Arnowitt-Deser-Misner mass and horizon angular velocity. Comparisons between the disk properties for both types of black holes are presented. The sequences of magnetized, equilibrium disks around Kerr black holes with scalar hair discussed in this study are morphologically and thermodynamically different than their Kerr black hole counterparts, namely their vertical size is larger, the high-density central region is more extended, and the fluid is more relativistic. Therefore, we expect significant differences to appear when these sequences are used as initial data for numerical relativity codes to investigate their dynamical (nonlinear) stability and used in tandem with ray-tracing codes to obtain synthetic images of black holes (i.e., shadows) in astrophysically relevant situations where the light source is provided by an emitting accretion disk.
Deliverable D2.1 (Black holes with scalar fields)

C A R Herdeiro, E Radu, K Uzawa arXiv:1811.10844 [hep-th] JHEP 1901 (2019) 215 (D1.2)

G Raposo, P Pani, M Bezares, C Palenzuela, V Cardoso arXiv:1811.07917 [gr-qc] Phys.Rev.D 99 (2019) 104072 (D1.2)

O Ramos, E Barausse arXiv:1811.07786 [gr-qc] Phys.Rev.D 99 (2019) 024034 (D3.1)

Constraints on Hořava gravity from binary black hole observations
Hořava gravity breaks Lorentz symmetry by introducing a preferred spacetime foliation, which is defined by a timelike dynamical scalar field, the khronon. The presence of this preferred foliation makes black hole solutions more complicated than in General Relativity, with the appearance of multiple distinct event horizons: a matter horizon for light/matter fields; a spin-0 horizon for the scalar excitations of the khronon; a spin-2 horizon for tensorial gravitational waves; and even, at least in spherical symmetry, a universal horizon for instantaneously propagating modes appearing in the ultraviolet. We study how black hole solutions in Hořava gravity change when the black hole is allowed to move with low velocity relative to the preferred foliation. These slowly moving solutions are a crucial ingredient to compute black hole “sensitivities” and predict gravitational wave emission (and, in particular, dipolar radiation) from the inspiral of binary black hole systems. We find that for generic values of the theory’s three dimensionless coupling constants, slowly moving black holes present curvature singularities at the universal horizon. Singularities at the spin-0 horizon also arise unless one waives the requirement of asymptotic flatness at spatial infinity. Nevertheless, we have verified that at least in a one-dimensional subset of the (three-dimensional) parameter space of the theory’s coupling constants, slowly moving black holes are regular everywhere, even though they coincide with the general-relativistic ones (thus implying, in particular, the absence of dipolar gravitational radiation). Remarkably, this subset of the parameter space essentially coincides with the one selected by the recent constraints from GW170817 and by solar system tests.
Deliverable D3.1 (Compact binary waveform)

D Gerosa, A Lima, E Berti, U Sperhake, M Kesden, R O'Shaughnessy arXiv:1811.05979 [gr-qc] Class.Quant.Grav. 36 (2018) 105003 (D3.1)

J G Rosa, L B Ventura arXiv:1811.05493 [hep-ph] Phys.Rev.Lett. 122 (2019) 161301 (D1.1), (D1.4)

T Harada, V Cardoso, D Miyata arXiv:1811.05179 [gr-qc] Phys.Rev.D 99 (2019) 044039 (D1.2), (D1.4)

Particle creation in gravitational collapse to a horizonless compact object
Black holes (BHs) play a central role in physics. However, gathering observational evidence for their existence is a notoriously difficult task. Current strategies to quantify the evidence for BHs all boil down to looking for signs of highly compact, horizonless bodies. Here, we study particle creation by objects which collapse to form ultracompact configurations, with the surface at an areal radius R = R_f satisfying 1 - (2M / R_f) = ε² ≪ 1 with M the object mass. We assume that gravitational collapse proceeds in a “standard” manner until R = R_f + 2Mε^2β, where β >r; 0, and then slows down to form a static object of radius R_f. In the standard collapsing phase, Hawking-like thermal radiation is emitted, which is as strong as the Hawking radiation of a BH with the same mass but lasts only for ∼40 (M / M_⊙) [44 + ln(10^-19 / ε)] μs. Thereafter, in a very large class of models, there exist two bursts of radiation separated by a very long dormant stage. The first burst occurs at the end of the transient Hawking radiation and is followed by a quiescent stage which lasts for ∼6 × 10⁶ (ε / 10⁻¹⁹)^-1(M / M_⊙) yr. Afterwards, the second burst is triggered, after which there is no more particle production and the star is forever dark. In a model with β = 1, both the first and second bursts outpower the transient Hawking radiation by a factor ∼10³⁸ (ε / 10^-19)^-2.
Deliverable D1.2 (Structure of stars with dark cores)
Deliverable D1.4 (Bounds on particle masses using gravity)

T Ikeda, R Brito, V Cardoso arXiv:1811.04950 [gr-qc] Phys.Rev.Lett. 122 (2019) 081101 (D1.1), (D1.4)

M Bošković, R Brito, V Cardoso, T Ikeda, H Witek arXiv:1811.04945 [gr-qc] Phys.Rev.D 99 (2019) 035006 (D1.4)

Axionic instabilities and new black hole solutions
The coupling between scalar and vector fields has a long and interesting history. Axions are one key possibility to solve the strong CP problem, and axionlike particles could be one solution to the dark matter puzzle. Extensive experimental and observational efforts are actively looking for "axionic" imprints. Given the nature of the coupling, and the universality of free fall, nontrivial important effects are expected in regions where gravity is strong. Rotating black holes (immersed, or not in magnetic fields) are a prime example of such regions. Here, we show the following: (i) A background electromagnetic field induces an axionic instability in flat space, for electric fields above a certain threshold value. Conversely, a homogeneous harmonic axion field induces an instability in the Maxwell sector. When carried over to curved spacetime, this phenomenon translates into generic instabilities of charged black holes. We describe the instability and its likely final state, new black hole solutions. (ii) In the presence of charge, black hole uniqueness results are lost. We find solutions that are small deformations of the Kerr-Newman geometry and hairy stationary solutions without angular momentum but which are "dragged" by the axion. Axion fields must exist around spinning black holes if these are immersed in external magnetic fields. The axion profile can be obtained perturbatively from the electrovacuum solution derived by Wald. (iii) Ultralight axions trigger superradiant instabilities of spinning black holes and form an axionic cloud in the exterior geometry. The superradiant growth can be interrupted or suppressed through couplings such as E ċ B (typical axionic coupling) but also more generic terms such as direct couplings to the invariant E²-B². These couplings lead to periodic bursts of light, which occur throughout the history of energy extraction from the black hole. We provide numerical and simple analytical estimates for the rates of these processes. (iv) Finally, we discuss how plasma effects can affect the evolution of superradiant instabilities.
Deliverable D1.4 (Bounds on particle masses using gravity)

A Maselli, P Pani, V Cardoso, T Abdelsalhin, L Gualtieri, V Ferrari arXiv:1811.03689 [gr-qc] Class.Quant.Grav. 36 (2019) 167001 (D3.1)

A Mangiagli, A Klein, A Sesana, E Barausse, M Colpi arXiv:1811.01805 [gr-qc] Phys.Rev.D 99 (2019) 064056 (D3.1)

Y Brihaye, C Herdeiro, E Radu arXiv:1810.09560 [gr-qc] Phys.Lett.B 788 (2019) 295-301 (D2.1)

The scalarised Schwarzschild-NUT spacetime
It has recently been suggested that vacuum black holes of General Relativity (GR) can become spontaneously scalarised when appropriate non-minimal couplings to curvature invariants are considered. These models circumvent the standard black hole no scalar hair theorems of GR, allowing both the standard GR solutions and new scalarised (a.k.a. hairy) solutions, which in some cases are thermodynamically preferred. Up to now, however, only (static and spherically symmetric) scalarised Schwarzschild solutions have been considered. It would be desirable to take into account the effect of rotation; however, the higher curvature invariants introduce a considerable challenge in obtaining the corresponding scalarised rotating black holes. As a toy model for rotation, we present here the scalarised generalisation of the Schwarzschild-NUT solution, taking either the Gauss–Bonnet (GB) or the Chern–Simons (CS) curvature invariant. The NUT charge n endows spacetime with "rotation", but the angular dependence of the corresponding scalarised solutions factorises, leading to a considerable technical simplification. For GB, but not for CS, scalarisation occurs for n = 0. This basic difference leads to a distinct space of solutions in the CS case, in particular exhibiting a double branch structure. In the GB case, increasing the horizon area demands a stronger non-minimal coupling for scalarisation; in the CS case, due to the double branch structure, both this and the opposite trend are found. We briefly comment also on the scalarised Reissner–Nordström-NUT solutions.
Deliverable D2.1 (Black holes with scalar fields)

H Witek, L Gualtieri, P Pani, T P Sotiriou arXiv:1810.05177 [gr-qc] Phys.Rev.D 99 (2019) 064035 (D3.1)

P Pani, L Gualtieri, T Abdelsalhin, X Jiménez-Forteza arXiv:1810.01094 [gr-qc] Phys.Rev.D 98 (2018) 124023 (D3.2)

R Luna, M Zilhão, V Cardoso, J L Costa, J Natário arXiv:1810.00886 [gr-qc] Phys.Rev.D 99 (2019) 064014 (D1.4)

L Annulli, L Bernard, D Blas, V Cardoso arXiv:1809.05108 [gr-qc] Phys.Rev.D 98 (2018) 084001 (D1.3)

C L Benone, L Crispino, C A R Herdeiro, M Richartz arXiv:1809.03952 [gr-qc] Phys.Rev.D 98 (2018) 124023 (D2.1), (D2.2)

V Cardoso, G Castro, A Maselli arXiv:1809.00673 [gr-qc] Phys.Rev.Lett. 121 (2018) 251103 (D1.4)

V Cardoso, M Kimura, A Maselli, L Senatore arXiv:1808.08962 [gr-qc] Phys.Rev.Lett. 121 (2018) 251105 (D3.3)

P V P Cunha, C A R Herdeiro, E Radu arXiv:1808.06692 [gr-qc] Phys.Rev.D 98 (2018) 104060 (D2.2)

V Cardoso, J L Costa, K Destounis, P Hintz arXiv:1808.03631 [gr-qc] Phys. Rev. D 98 (2018) 104007 (D2.2)

W G Cook, D Wang, U Sperhake arXiv:1808.05834 [gr-qc] Class.Quant.Grav. 35 (2018) 235008 (D4.3), (D4.4)

C Herdeiro, I Perapechka, E Radu, Y Shnir arXiv:1808.05388 [gr-qc] JHEP 1810 (2018) 119 (D2.1)

Skyrmions around Kerr black holes and spinning BHs with Skyrme hair
We study solutions of the Einstein-Skyrme model. Firstly we consider test field Skyrmions on the Kerr background. These configurations - hereafter dubbed Skerrmions - can be in equilibrium with a Kerr black hole (BH) by virtue of a synchronisation condition. We consider two sectors for Skerrmions. In the sector with non-zero baryon charge, Skerrmions are akin to the known Skyrme solutions on the Schwarzschild background. These "topological" configurations reduce to flat spacetime Skyrmions in a vanishing BH mass limit, moreoever, they never become "small" perturbations on the Kerr background: the non-linearities of the Skyrme model are crucial for all such Skerrmions. In the non-topological sector, on the other hand, Skerrmions have no analogue on the Schwarzschild background. Non-topological Skerrmions carry not baryon charge and bifurcate from a subset of Kerr solutions defining an existence line. Therein the appropriate truncation of the Skyrme model yield a linear scalar field theory containing a complex plus a real field, both massive and decoupled, and the Skerrmions reduce to the known stationary scalar clouds around Kerr BHs. Moreover, non-topological Skerrmions trivialise in the vanishing BH mass limit. We then discuss the backreaction of these Skerrmions, that yield rotating BHs with synchronised Skyrme hair, which continously connect to the Kerr solution (self-gravitating Skyrmions) in the non-topological (topological) sector. In particular, the non-topological hairy BHs provide a non-linear realisation, within the Skyrme model, of the synchronous stationary scalar clouds around Kerr.
Deliverable D2.1 (Black holes with scalar fields)

X Jiménez-Forteza, T Abdelsalhin, P Pani, L Gualtieri arXiv:1807.08016 [gr-qc] Phys.Rev.D 98 (2018) 124014 (D3.1)

T Assumpçao, V Cardoso, A Ishibashi, M Richartz, M Zilhão arXiv:1806.07909 [gr-qc] Phys.Rev.D 99 (2018) 064036 (D2.4)

N Sanchis-Gual, C Herdeiro, J A Font, E Radu, F Di Giovanni arXiv:1806.07779 [gr-qc] Phys.Rev.D 99 (2019) 024017 (D2.2)

Head-on collisions and orbital mergers of Proca stars
Proca stars, aka vector boson stars, are self-gravitating Bose-Einstein condensates obtained as numerical stationary solutions of the Einstein-(complex)-Proca system. These solitonic objects can achieve a compactness comparable to that of black holes, thus yielding an example of a black hole mimicker, which, moreover, can be both stable and form dynamically from generic initial data by the mechanism of gravitational cooling. In this paper we further explore the dynamical properties of these solitonic objects by performing both head-on collisions and orbital mergers of equal mass Proca stars, using fully nonlinear numerical evolutions. For the head-on collisions, we show that the end point and the gravitational waveform from these collisions depends on the compactness of the Proca star. Proca stars with sufficiently small compactness collide emitting gravitational radiation and leaving a stable Proca star remnant. But more compact Proca stars collide to form a transient hypermassive Proca star, which ends up decaying into a black hole, albeit temporarily surrounded by Proca quasibound states. The unstable intermediate stage can leave an imprint in the waveform, making it distinct from that of a head-on collision of black holes. The final quasinormal ringing matches that of Schwarzschild black hole, even though small deviations may occur, as a signature of sufficiently nonlinear and long-lived Proca quasibound states. For the orbital mergers, we have considered eccentric orbits and the outcome also depends on the compactness of the stars. For the binaries with the most compact stars, the binary merger forms a Kerr black hole which retains part of the initial orbital angular momentum, being surrounded by a transient Proca field remnant; in cases with lower compactness, the binary merger forms a massive Proca star with angular momentum, but out of equilibrium. As in previous studies of (scalar) boson stars, the angular momentum of such objects appears to converge to zero as a final equilibrium state is approached.
Deliverable D2.2 (Black holes with gauge fields)

M Bošković, F Duque, M C Ferreira, F S Miguel, V Cardoso arXiv:1806.07331 [gr-qc] Phys.Rev.D 98 (2018) 024037 (D1.4)

T Delsate, C Herdeiro, E Radu arXiv:1806.06700 [gr-qc] Phys.Lett.B 787 (2018) 8-15 (D3.1)

L Barack et al arXiv:1806.05195 [gr-qc] Class.Quant.Grav. 36 (2019) 143001 (D3.1), (D3.2), (D3.3)

C A R Herdeiro, R Radu, N Sanchis-Gual, J A Font arXiv:1806.05190 [gr-qc] Phys.Rev.Lett. 121 (2018) 101102 (D2.1), (D2.2)

V Korol, E M Rossi, E Barausse arXiv:1806.03306 [astro-ph] MNRAS 483 (2019) 5518-5533 (D3.2)

A multi-messenger study of the Milky Way's stellar disc and bulge with LISA, Gaia and LSST
The upcoming Laser Interferometer Space Antenna (LISA) mission offers the unique opportunity to study the Milky Way through gravitational wave (GW) radiation from a large population of Galactic binaries. Among the variety of Galactic GW sources, LISA is expected to individually resolve signals from ∼10⁵ ultra-compact double white dwarf (DWD) binaries. DWDs detected by LISA will be distributed across the Galaxy, including regions that are hardly accessible to electromagnetic (EM) observations such as the inner part of the Galactic disc, the bulge, and beyond. We quantitatively show that the large number of DWD detections will allow us to use these systems as tracers of the Milky Way potential. We demonstrate that density profiles of DWDs detected by LISA may provide constraints on the scale length parameters of the baryonic components that are both accurate and precise, with statistical errors of a few per cent to 10 per cent level. Furthermore, the LISA sample is found to be sufficient to disentangle between different (commonly used) disc profiles, by well covering the disc out to sufficiently large radii. Finally, up to ∼80 DWDs can be detected through both EM and GW radiation. This enables multimessenger astronomy with DWD binaries and allows one to extract their physical properties using both probes. We show that fitting the Galactic rotation curve constructed using distances inferred from GWs and proper motions from optical observations yield a unique and competitive estimate of the bulge mass. Instead robust results for the stellar disc mass are contingent upon knowledge of the dark matter content.
Deliverable D3.2 (Astrophysical Observables)

E Barausse, R Brito, V Cardoso, I Dvorkin, P Pani arXiv:1805.08229 [gr-qc] Class.Quant.Grav. 35 (2018) 20LT01 (D1.4)

M Bastero-Gil, A Berera, R Hernández-Jiménez, J G Rosa arXiv:1805.07186 [astro-ph] Phys.Rev.D 98 (2018) 083502 (D1.1), (D1.4)

P V P Cunha, C A R Herdeiro, M J Rodriguez arXiv:1805.03798 [gr-qc] Phys.Rev.D 98 (2018) 044053 (D2.4)

T Abdelsalhin, L Gualtieri, P Pani arXiv:1805.01487 [gr-qc] Phys.Rev.D 98 (2018) 104046 (D3.1)

L F O Costa, R Franco, V Cardoso arXiv:1805.01097 [gr-qc] Phys.Rev.D 98 (2018) 024026 (D3.2)

J F M Delgado, C A R Herdeiro, E Radu arXiv:1804.04910 [gr-qc] Phys.Rev.D 97 (2018) 124012 (D2.1)

D P Mihaylov, C J Moore, J R Gair, A Lasenby, G Gilmore arXiv:1804.00660 [gr-qc] Phys.Rev.D 97 (2018) 124058 (D3.2)

Y Brihaye, T Delplace, C Herdeiro, E Radu arXiv:1803.09089 [gr-qc] Phys.Lett.B 782 (2018) 124-130 (D2.1), (D2.2)

C A R Herdeiro, E Radu arXiv:1803.08149 [gr-qc] Int.J.Mod.Phys.D 27 (2018) 1843009 (D2.1)

R Vicente, V Cardoso, J C Lopes arXiv:1803.08060 [gr-qc] Phys. Rev. D 97 (2018) 0840329 (D1.1)

F Di Giovanni, N Sanchis-Gual, C A R Herdeiro, J A Font arXiv:1803.04802 [gr-qc] Phys.Rev.D 98 (2018) 064044 (D2.2)

V Cardoso, T Ikeda, C J Moore, C-M Yoo arXiv:1803.03271 [gr-qc] Phys.Rev.D 97 (2018) 084013 (D4.4)

M R Correia, V Cardoso arXiv:1802.07735 [gr-qc] Phys.Rev.D 97 (2018) 084030 (D1.2)

P V P Cunha, C A R Herdeiro, M J Rodriguez arXiv:1802.02675 [gr-qc] Phys.Rev.D 97 (2018) 084020 (D2.3)

V Cardoso, O J C Dias, G S Hartnett, M Middleton, P Pani, J E Santos arXiv:1801.01420 [gr-qc] JCAP 1803 (2018) 043 (D1.1), (D2.2)

Constraining the mass of dark photons and axion-like particles through black-hole superradiance
Ultralight bosons and axion-like particles appear naturally in different scenarios and could solve some long-standing puzzles. Their detection is challenging, and all direct methods hinge on unknown couplings to the Standard Model of particle physics. However, the universal coupling to gravity provides model-independent signatures for these fields. We explore here the superradiant instability of spinning black holes triggered in the presence of such fields. The instability taps angular momentum from and limits the maximum spin of astrophysical black holes. We compute, for the first time, the spectrum of the most unstable modes of a massive vector (Proca) field for generic black-hole spin and Proca mass. The observed stability of the inner disk of stellar-mass black holes can be used to derive direct constraints on the mass of dark photons in the mass range 10⁻¹³ eV ≲ m_V ≲ 3 × 10⁻¹² eV. By including also higher azimuthal modes, similar constraints apply to axion-like particles in the mass range 6 × 10⁻¹³ eV ≲ m_ALP ≲ 10⁻¹¹ eV. Likewise, mass and spin distributions of supermassive BHs -- as measured through continuum fitting, Kα iron line, or with the future space-based gravitational-wave detector LISA -- imply indirect bounds in the mass range approximately 10⁻¹⁹ eV ≲ m_V, m_ALP ≲ 10⁻¹³ eV, for both axion-like particles and dark photons. Overall, superradiance allows to explore a region of approximately 8 orders of magnitude in the mass of ultralight bosons.
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D2.2 (Black holes with gauge fields)

P V P Cunha, C A R Herdeiro arXiv:1801.00860 [gr-qc] Gen.Rel.Grav. 50 (2018) 42 (D2.3), (D2.4)

C Herdeiro, J Kunz, E Radu, B Subagyo arXiv:1712.04286 [gr-qc] Phys.Lett.B 779 (2018) 151 (D2.1), (D2.2)

C Guépin, K Kotera, E Barausse, K Fang, K Maruse arXiv:1711.11274 [astro-ph] Astron.&Astroph. 616 (2018) A179 (D3.2)

V Cardoso, J L Costa, K Destounis, P Hintz, A Jansen arXiv:1711.10502 [gr-qc] Phys.Rev.Lett. 120 (2018) 031103 (D1.1), (D2.1)

M Bastero-Gil, A Berera, R O Ramos, J G Rosa arXiv:1711.09023 [hep-ph] JHEP 1802 (2018) 063 (D1.1), (D1.4)

E A Huerta, C J Moore, et al arXiv:1711.06276 [gr-qc] Phys.Rev.D 97 (2018) 024031 (D3.1)

ENIGMA: Eccentric, Non-spinning, Inspiral Gaussian-process Merger Approximant for the characterization of eccentric binary black hole mergers
We present 𝙴𝙽𝙸𝙶𝙼𝙰, a time domain, inspiral-merger-ringdown waveform model that describes non-spinning binary black holes systems that evolve on moderately eccentric orbits. The inspiral evolution is described using a consistent combination of post-Newtonian theory, self-force and black hole perturbation theory. Assuming moderately eccentric binaries that circularize prior to coalescence, we smoothly match the eccentric inspiral with a stand-alone, quasi-circular merger, which is constructed using machine learning algorithms that are trained with quasi-circular numerical relativity waveforms. We show that 𝙴𝙽𝙸𝙶𝙼𝙰 reproduces with excellent accuracy the dynamics of quasi-circular compact binaries. We validate 𝙴𝙽𝙸𝙶𝙼𝙰 using a set of 𝙴𝚒𝚗𝚜𝚝𝚎𝚒𝚗 𝚃𝚘𝚘𝚕𝚔𝚒𝚝 eccentric numerical relativity waveforms, which describe eccentric binary black hole mergers with mass-ratios between 1 ≤ q ≤ 5.5, and eccentricities e₀ ≲ 0.2 ten orbits before merger. We use this model to explore in detail the physics that can be extracted with moderately eccentric, non-spinning binary black hole mergers. In particular, we use 𝙴𝙽𝙸𝙶𝙼𝙰 to show that the gravitational wave transients GW150914, GW151226, GW170104 and GW170814 can be effectively recovered with spinning, quasi-circular templates if the eccentricity of these events at a gravitational wave frequency of 10Hz satisfies e₀ ≤ {0.175,0.125,0.175,0.175}, respectively. We show that if these systems have eccentricities e₀ ∼ 0.1 at a gravitational wave frequency of 10Hz, they can be misclassified as quasi-circular binaries due to parameter space degeneracies between eccentricity and spin corrections.
Deliverable D3.1 (Compact binary waveform)

H O Silva, J Sakstein, L Gualtieri, T P Sotiriou, E Berti arXiv:1711.02080 [gr-qc] Phys.Rev.Lett. 120 (2018) 131104 (D3.3)

M Wang, C Herdeiro, J Jing arXiv:1710.10461 [gr-qc] Phys.Rev.D 96 (2017) 104035 (D2.1), (D2.2)

C Palenzuela, P Pani, M Bezares, V Cardoso, L Lehner, S Liebling arXiv:1710.09432 [gr-qc] Phys.Rev.D 96 (2017) 104058 (D1.2), (D2.3)

C Dappiaggi, H R C Ferreira, C A R Herdeiro arXiv:1710.08039 [gr-qc] Phys.Lett.B 778 (2018) 146 (D1.1)

Y Brihaye, C Herdeiro, E Radu, D H Tchrakian arXiv:1710.03833 [gr-qc] JHEP 11 (2017) 037 (D2.1), (D2.2)

V Baibhav, E Berti, V Cardoso, G Khanna arXiv:1710.02156 [gr-qc] Phys.Rev.D 97 (2018) 044048--> (D2.1), (D3.2)

Black Hole Spectroscopy: Systematic Errors and Ringdown Energy Estimates
The relaxation of a distorted black hole to its final state provides important tests of general relativity within the reach of current and upcoming gravitational wave facilities. In black hole perturbation theory, this phase consists of a simple linear superposition of exponentially damped sinusoids (the quasinormal modes) and of a power-law tail. How many quasinormal modes are necessary to describe waveforms with a prescribed precision? What error do we incur by only including quasinormal modes, and not tails? What other systematic effects are present in current state-of-the-art numerical waveforms? These issues, which are basic to testing fundamental physics with distorted black holes, have hardly been addressed in the literature. We use numerical relativity waveforms and accurate evolutions within black hole perturbation theory to provide some answers. We show that (i) a determination of the fundamental l = m = 2 quasinormal mode to within 1% or better requires the inclusion of at least the first overtone, and preferably of the first two or three overtones; (ii) a determination of the black hole mass and spin with precision better than 1% requires the inclusion of at least two quasinormal modes for any given angular harmonic mode (ℓ,m). We also improve on previous estimates and fits for the ringdown energy radiated in the various multipoles. These results are important to quantify theoretical (as opposed to instrumental) limits in parameter estimation accuracy and tests of general relativity allowed by ringdown measurements with high signal-to-noise ratio gravitational wave detectors.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D3.2 (Astrophysical Observables)

M C Ferreira, C F B Macedo, V Cardoso arXiv:1710.00830 [gr-qc] Phys.Rev.D 96 (2017) 083017 (D1.2)

W G Cook, U Sperhake, E Berti, V Cardoso arXiv:1709.10514 [gr-qc] Phys.Rev.D 96 (2017) 124006 (D4.1), (D4.2)

J Alsing, H O Silva, E Berti arXiv:1709.07889 [astro-ph] MNRAS 478 (2018) 1377-1391 (D1.2), (D3.2)

Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state
We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multi-modality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be 2.06 M_⊙ < m_max < 2.24M_⊙ (68%), 2.0 M_⊙ < m_max < 2.5M_⊙ (90%), where this constraint is robust against the choice of model for the mass distribution and to removing the most extreme (highest mass) neutron stars from the dataset. If this sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts tight constraints on the equation of state. For a set of realistic equations of state that support > 2 M_⊙ neutron stars, our inference of mmax is able to distinguish between models at odds ratios of up to 15:1, whilst under a flexible piecewise polytropic equation of state model our maximum mass measurement improves constraints on the pressure at 3−7 × the nuclear saturation density by ∼35−50% compared to simply requiring m_max > 2M_⊙. We obtain a lower bound on the maximum sound speed attained inside the neutron star of c^max_s > 0.64c (99.8%), ruling out c_s^max < c / √3 at high significance.Our constraints on the equation of state strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.
Deliverable D1.2 (Structure of stars with dark cores)
Deliverable D3.2 (Astrophysical Observables)

K Glampedakis, L Gualtieri arXiv:1709.07049 [astro-ph] Astr.Space Sci.Libr. 457 (2018) 673-736 (D3.1)

J G Rosa, T W Kephart arXiv:1709.06581 [gr-qc] Phys.Rev.Lett. 120 (2018) 231102 (D1.1)

P V P Cunha, J A Font, C Herdeiro, E Radu, N Sanchis-Gual, M Zilhão arXiv:1709.06118 [gr-qc] Phys.Rev.D 96 (2017) 104040 (D1.2)

M Bonetti, A Sesana, E Barausse, F Haardt arXiv:1709.06095 [astro-ph] MNRAS 477 (2018) 2599-2612 (D3.1)

Post-Newtonian evolution of massive black hole triplets in galactic nuclei -- III. A robust lower limit to the nHz stochastic background of gravitational waves
Inspiraling massive black-hole binaries (MBHBs) forming in the aftermath of galaxy mergers are expected to be the loudest gravitational-wave (GW) sources relevant for pulsar-timing arrays (PTAs) at nHz frequencies. The incoherent overlap of signals from a cosmic population of MBHBs gives rise to a stochastic GW background (GWB) with characteristic strain around h_c ∼ 10⁻¹⁵ at a reference frequency of 1 yr⁻¹, although uncertainties around this value are large. Current PTAs are piercing into the GW amplitude range predicted by state-of-the-art MBHB-population models, but no detection has been reported so far. To assess the future success prospects of PTA experiments, it is therefore important to estimate the minimum GWB level consistent with our current understanding of the formation and evolution of galaxies and massive black holes (MBHs). To this purpose, we couple a state-of-the-art semianalytic model of galaxy evolution and an extensive study of the statistical outcome of triple MBH interactions. We show that even in the most pessimistic scenario where all MBHBs stall before entering the GW-dominated regime, triple interactions resulting from subsequent galaxy mergers inevitably drive a considerable fraction of the MBHB population to coalescence. In the nHz frequency range relevant for PTA, the resulting GWB is only a factor of 2-to-3 suppressed compared to a fiducial model where binaries are allowed to merge over Gyr timescales after their host galaxies merge. Coupled with current estimates of the expected GWB amplitude range, our findings suggest that the minimum GWB from cosmic MBHBs is unlikely to be lower than h_c ∼ 10⁻¹⁶ (at f = 1 yr⁻¹), well within the expected sensitivity of projected PTAs based on future observations with FAST, MeerKAT and SKA.
Deliverable D3.1 (Compact binary waveform)

M Bonetti, F Haardt, A Sesana, E Barausse arXiv:1709.06088 [astro-ph] MNRAS 477 (2018) 3910-3926 (D3.1)

Post-Newtonian evolution of massive black hole triplets in galactic nuclei -- II. Survey of the parameter space
Massive black hole binaries (MBHBs) are expected to form at the centre of merging galaxies during the hierarchical assembly of the cosmic large scale structure, and are therefore expected to be the loudest sources of gravitational waves (GWs) in the frequency window from nHz to tens of mHz. However, because of the dearth of relevant energy exchanges with background stars and gas, many of these MBHBs may stall at separations too large for GW emission to drive them to coalescence in less than a Hubble time. Triple MBH systems are then bound to form after a further galaxy merger, triggering a complex and rich dynamics that can eventually lead to MBH coalescence. Here we report on the results of a large set of numerical simulations performed with the code presented in Bonetti et al. (2016) where MBH triplets are set in spherical stellar potentials and MBH dynamics is followed through 2.5 post-Newtonian order in the equations of motion. We characterise each simulated system by the mass of the heavier MBH, the inner and outer mass ratios, the initial eccentricities of the inner and outer binaries, and the relative inclination, running a total of about 15k simulations. From our full suite of simulated systems we find that a fraction 20-30% of the MBH binaries that would otherwise stall are led to coalesce within a Hubble time. The corresponding coalescence timescale has a log-normal distribution, with a mean value around 250 Myr, while the eccentricity close to the plunge, albeit small, is non-negligible (∼0.1). We construct and discuss marginalised probability distributions of the main parameters involved and, in a companion paper, we will use the results presented here to forecast the contribution of MBH triplets to the GW signal in the nHz regime probed by PTA experiments. In a follow-up paper, we will perform a similar exercise for MBHBs in the mHz regime targeted by LISA.
Deliverable D3.1 (Compact binary waveform)

V Cardoso, P Pani arXiv:1709.01525 [gr-qc] Nat.Astron.1 (2017) 586-591 (D1.2)

C A R Herdeiro, A M Pombo, E Radu arXiv:1708.05674 [gr-qc] Phys.Lett.B 773 (2017) 654-662 (D2.1), (D2.2)

P V P Cunha, E Berti, C A R Herdeiro arXiv:1708.04211 [gr-qc] Phys.Rev.Lett. 119 (2017) 251102 (D1.2)

U Sperhake, C J Moore, R Rosca, M Agathos, D Gerosa, C D Ott arXiv:1708.03651 [gr-qc] Phys.Rev.Lett. 119 (2017) 201103 (D3.3)

T Ikeda, C-M Yoo, V Cardoso arXiv:1708.01344 [gr-qc] Phys.Rev.D 96 (2017) 064047 (D1.2)

V Cardoso, T Houri, M Kimura arXiv:1707.08534 [hep-th] Class.Quant.Grav. 35 (2018) 015011 (D1.1), (D2.1)

H R C Ferreira, C A R Herdeiro arXiv:1707.08133 [gr-qc] Phys.Lett.B 773 (2017) 129-134 (D2.1)

C J Moore, D Mihaylov, A Lasenby, G Gilmore arXiv:1707.06239 [astro-ph] Phys.Rev.Lett. 119 (2017) 261102 (D3.2)

M Bonetti, E Barausse, G Faye, F Haardt, A Sesana arXiv:1707.04902 [gr-qc] Class.Quant.Grav. 32 (2017) 215004 (D3.1)

V Cardoso, P Pani arXiv:1707.03021 [gr-qc] (D1.2)

K Glampedakis, G Pappas, H O Silva, E Berti arXiv:1706.07658 [hep-th] Phys.Rev.D 96 (2017) 064054 (D1.2), (D3.1)

V Cardoso, T Houri, M Kimura arXiv:1706.07339 [hep-th] Phys.Rev.D 96 (2017) 024044 (D1.1), (D2.1)

C A R Herdeiro, E Radu arXiv:1706.06597 [gr-qc] Phys.Rev.Lett. 119 (2017) 261101 (D2.2)

R Brito, S Ghosh, E Barausse, E Berti, V Cardoso, I Dvorkin, A Klein, P Pani arXiv:1706.06311 [gr-qc] Phys.Rev.D 96 (2017) 064050 (D1.1), (D3.1)

Gravitational wave searches for ultralight bosons with LIGO and LISA
Ultralight bosons can induce superradiant instabilities in spinning black holes, tapping their rotational energy to trigger the growth of a bosonic condensate. Possible observational imprints of these boson clouds include (i) direct detection of the nearly monochromatic (resolvable or stochastic) gravitational waves emitted by the condensate, and (ii) statistically significant evidence for the formation of "holes" at large spins in the spin versus mass plane (sometimes also referred to as "Regge plane") of astrophysical black holes. In this work, we focus on the prospects of LISA and LIGO detecting or constraining scalars with mass in the range m_s ∈ [10⁻¹⁹,10⁻¹⁵] eV and m_s ∈ [10⁻¹⁴,10⁻¹¹] eV, respectively. Using astrophysical models of black-hole populations and black-hole perturbation theory calculations of the gravitational emission, we find that LIGO could observe a stochastic background of gravitational radiation in the range m_s ∈ [2&yimes;10⁻¹³,10⁻¹²] eV, and up to ∼10⁴ resolvable events in a 4-year search if m_s ∼ 3×10⁻¹³ eV. LISA could observe a stochastic background for boson masses in the range m_s ∈ [5×10⁻¹⁹,5×10⁻¹⁶], and up to ∼10³ resolvable events in a 4-year search if ms ∼ 10⁻¹⁷ eV. LISA could further measure spins for black-hole binaries with component masses in the range [10³,10⁷] M_⊙, which is not probed by traditional spin-measurement techniques. A statistical analysis of the spin distribution of these binaries could either rule out scalar fields in the mass range [4×10⁻¹⁸,10⁻¹⁴] eV, or measure ms with ten percent accuracy if light scalars in the mass range [10⁻¹⁷,10⁻¹³] eV exist.
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D3.1 (Compact binary waveform)

R Brito, S Ghosh, E Barausse, E Berti, V Cardoso, I Dvorkin, A Klein, P Pani arXiv:1706.05097 [gr-qc] Phys.Rev.Lett. 119 (2017) 131101 (D1.1), (D3.1)

H Bantilan, P Figueras, M Kunesch, P Romatschke arXiv:1706.04199 [hep-th] Phys.Rev.Lett. 119 (2017) 191103 (D4.2)

S Hopper, V Cardoso arXiv:1706.02791 [gr-qc] Phys.Rev.D 97 (2018) 044031 (D3.1)

M Richartz, C A R Herdeiro, E Berti arXiv:1706.01112 [gr-qc] Phys.Rev.D 96 (2017) 044034 (D2.3)

C Herdeiro, V Paturyan, E Radu, D H Tchrakian arXiv:1705.07979 [gr-qc] Phys.Lett.B 772 (2017) 63-69 (D2.2)

P V P Cunha, C A R Herdeiro, E Radu arXiv:1705.05461 [gr-qc] Phys.Rev.D 96 (2017) 024039 (D2.3)

A Chua, C J Moore, J R Gair arXiv:1705.04259 [gr-qc] Phys.Rev.D 96 (2017) 044005 (D3.1)

J M Fedrow, C D Ott, U Sperhake, J Blackman, R Haas, C Reisswig, A De Felice arXiv:1704.07383 [astro-ph] Phys.Rev.Lett. 119 (2017) 171103 (D3.1), (D3.2)

V Cardoso, P Pani, Y Tien-Tien arXiv:1704.06151 [astro-ph] Phys.Rev.D 95 (2017) 124056 (D1.1), (D1.4)

G Camelio, A Lovato, L Gualtieri, O Benhar, J A Pons, V Ferrari arXiv:1704.01923 [astro-ph] Phys.Rev.D 96 (2017) 043015 (D3.2)

J Gair et al. arXiv:1704.00009 [astro-ph] J.Phys.Conf.Ser. 840 (2017) 012021 (D3.1), (D3.2)

A Maselli, P Pani, R Cotesta, L Gualtieri, V Ferrari, L Stella arXiv:1703.01472 [gr-qc] Astrophys.J 843 (2017) 25 (D3.2)

A Maselli, P Pani, V Cardoso, T Abdelsalhin, L Gualtieri, V Ferrari arXiv:1703.10612 [astro-ph] Phys.Rev.Lett. 120 (2018) 081101 (D1.2)

S Babak et al. arXiv:1703.09722 [gr-qc] Phys.Rev.D 95 (2017) 103012 (D3.1), (D3.2)

M Zhou, C Bambi, C A R Herdeiro, E Radu arXiv:1703.06836 [gr-qc] Phys.Rev.D 95 (2017) 104035 (D2.2)

D Gerosa, E Berti arXiv:1703.06223 [gr-qc] Phys.Rev.D 95 (2017) 124046 (D3.1), (D3.2)

I Dvorkin, E Barausse arXiv:1702.06964 [astro-ph] MNRAS 470 (2017) 4547-4556 (D3.1), (D3.2)

The nightmare scenario: measuring the stochastic gravitational-wave background from stalling massive black-hole binaries with pulsar-timing arrays
Massive black-hole binaries, formed when galaxies merge, are among the primary sources of gravitational waves targeted by ongoing Pulsar Timing Array (PTA) experiments and the upcoming space-based LISA interferometer. However, their formation and merger rates are still highly uncertain. Recent upper limits on the stochastic gravitational-wave background obtained by PTAs are starting being in marginal tension with theoretical models for the pairing and orbital evolution of these systems. This tension can be resolved by assuming that these binaries are more eccentric or interact more strongly with the environment (gas and stars) than expected, or by accounting for possible selection biases in the construction of the theoretical models. However, another (pessimistic) possibility is that these binaries do not merge at all, but stall at large (∼ pc) separations. We explore this extreme scenario by using a galaxy-formation semi-analytic model including massive black holes (isolated and in binaries), and show that future generations of PTAs will detect the stochastic gravitational-wave background from the massive black-hole binary population within 10−15 years of observations, even in the "nightmare scenario" in which all binaries stall at the hardening radius. Moreover, we argue that this scenario is too pessimistic, because our model predicts the existence of a sub-population of binaries with small mass ratios (q ≲ 10⁻³) that should merge within a Hubble time simply as a result of gravitational-wave emission. This sub-population will be observable with large signal-to-noise ratios by future PTAs thanks to next-generation radiotelescopes such as SKA or FAST, and possibly by LISA.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)

N Sanchis-Gual, C Herdeiro, E Radu, J C Degollado, J A Font arXiv:1702.04532 [astro-ph] Phys.Rev.D 95 (2017) 104028 (D2.2)

E Barausse, F Shankar, M Bernardi, Y Dubois, R K Sheth arXiv:1702.01762 [astro-ph] MNRAS 468 (2017) 4782-4791 (D3.1), (D3.2)

Selection bias in dynamically-measured supermassive black hole samples: Scaling relations and correlations between residuals in semi-analytic galaxy formation models
Recent work has confirmed that the masses of supermassive black holes, estimated from scaling relations with global properties such as the stellar masses of their host galaxies, may be biased high. Much of this may be caused by the requirement that the gravitational sphere of influence of the black hole must be resolved for the black-hole mass to be reliably estimated. We revisit this issue by using a comprehensive galaxy evolution semi-analytic model, which self-consistently evolves supermassive black holes from high-redshift seeds via gas accretion and mergers, and also includes AGN feedback. Once tuned to reproduce the (mean) correlation of black-hole mass with velocity dispersion, the model is unable to also account for the correlation with stellar mass. This behaviour is independent of the model's parameters, thus suggesting an internal inconsistency in the data. The predicted distributions, especially at the low-mass end, are also much broader than observed. However, if selection effects are included, the model's predictions tend to align with the observations. We also demonstrate that the correlations between the residuals of the local scaling relations are more effective than the scaling relations themselves at constraining AGN feedback models. In fact, we find that our semi-analytic model, while in apparent broad agreement with the scaling relations when accounting for selection biases, yields very weak correlations between their residuals at fixed stellar mass, in stark contrast with observations. This problem persists when changing the AGN feedback strength, and is also present in the z ∼ 0 outputs of the hydrodynamic cosmological simulation Horizon-AGN, which includes state-of-the-art treatments of AGN feedback. This suggests that current AGN feedback models may be too weak or are simply not capturing the effect of the black hole on the stellar velocity dispersion.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)

P Figueras, M Kunesch, L Lehner, S Tunyasuvunakool arXiv:1702.01755 [hep-th] Phys.Rev.Lett. 118 (2017) 151103 (D4.4)

J P Conlon, C A R Herdeiro arXiv:1701.02034 [gr-qc] Phys.Lett.B 780 (2018) 169-173 (D1.1), (D2.1)

V Cardoso, E Franzin, A Maselli, P Pani, G Raposo arXiv:1701.01116 [gr-qc] Phys.Rev.D 95 (2017) 084014 (D1.2), (D1.4)

T Shen, M Zhou, C Bambi, C A R Herdeiro, E Radu arXiv:1701.00192 [gr-qc] JCAP 1708 (2017) 014 (D2.2)

P V P Cunha, C A R Herdeiro, B Kleihaus, J Kunz, E Radu arXiv:1701.00079 [gr-qc] Phys.Lett.B 768 (2017) 373-379 (D2.3)

D Gerosa, U Sperhake, J Vosmera arXiv:1612.05263 [gr-qc] Class.Quantum Grav. 34 (2017) 064004 (D3.1)

M Bastero-Gil, A Berera, R Brandenberger, I G Moss, R O Ramos, J G Rosa arXiv:1612.04726 [astro-ph] JCAP 1801 (2018) 002 (D1.1), (D1.4)

K Belczynski, T Ryu, R Perna, E Berti, T L Tanaka, T Bulik arXiv:1612.01524 [gr-qc] MNRAS 471 (2017) 4702-4721 (D3.1), (D3.2)

On the likelihood of detecting gravitational waves from Population III compact object binaries
We study the contribution of binary black hole (BH-BH) mergers from the first, metal-free stars in the Universe (Pop III) to gravitational wave detection rates. Our study combines initial conditions for the formation of Pop III stars based on N-body simulations of binary formation (including rates, binary fraction, initial mass function, orbital separation and eccentricity distributions) with an updated model of stellar evolution specific for Pop III stars. We find that the merger rate of these Pop III BH-BH systems is relatively small (< 0.1 Gpc^-3 yr^-1) at low redshifts (z < 2), where it can be compared with the LIGO empirical estimate of 9-240 Gpc^-3 yr^-1 (Abbott et al. 2016). The predicted rates are even smaller for Pop III double neutron star and black hole neutron star mergers. Our rates are compatible with those of Hartwig et al. (2016), but significantly smaller than those found in previous work (Bond & Carr 1984; Belczynski et al. 2004; Kinugawa et al. 2014, 2016). We explain the reasons for this discrepancy by means of detailed model comparisons and point out that (i) identification of Pop III BH-BH mergers may not be possible by advanced LIGO, and (ii) the level of stochastic gravitational wave background from Pop III mergers may be lower than recently estimated (Kowalska et al. 2012; Inayoshi et al. 2016; Dvorkin et al. 2016). We further estimate gravitational wave detection rates for third-generation interferometric detectors. Our calculations are relevant for low to moderately rotating Pop III stars. We can now exclude significant (> 1 per cent) contribution of these stars to low-redshift BH-BH mergers. However, it remains to be tested whether (and at what level) rapidly spinning Pop III stars (homogeneous evolution) can contribute to BH-BH mergers in the local Universe.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)

R Fujita, V Cardoso arXiv:1612.00978 [gr-qc] Phys.Rev.D 95 (2017) 044016 (D1.3), (D3.3)

N Franchini, P Pani, A Maselli, L Gualtieri, C A R Herdeiro, E Radu, V Ferrari arXiv:1612.00038 [astro-ph] Phys.Rev.D 95 (2017) 124025 (D2.1), (D3.2)

N Sanchis-Gual, J C Degollado, J A Font, C Herdeiro, E Radu arXiv:1611.02441 [gr-qc] Class.Quant.Grav.34 (2017) 165001 (D2.2)

P V P Cunha, J Grover, C Herdeiro, E Radu, H Runarsson, A Wittig arXiv:1609.01340 [gr-qc] Phys.Rev.D 94 (2016) 104023 (D2.1), (D2.3)

Chaotic lensing around boson stars and Kerr black holes with scalar hair
In a recent letter, arXiv:1509.00021, it was shown that the lensing of light around rotating boson stars and Kerr black holes with scalar hair can exhibit chaotic patterns. Since no separation of variables is known (or expected) for geodesic motion on these backgrounds, we examine the 2D effective potentials for photon trajectories, to obtain a deeper understanding of this phenomenon. We find that the emergence of stable light rings on the background spacetimes, allows the formation of "pockets" in one of the effective potentials, for open sets of impact parameters, leading to an effective trapping of some trajectories, dubbed quasi-bound orbits. We conclude that pocket formation induces chaotic scattering, although not all chaotic orbits are associated to pockets. These and other features are illustrated in a gallery of examples, obtained with a new ray-tracing code, PYHOLE, which includes tools for a simple, simultaneous visualization of the effective potential together with the spacetime trajectory, for any given point in a lensing image. An analysis of photon orbits allows us to further establish a positive correlation between photon orbits in chaotic regions and those with more than one turning point in the radial direction; we recall that the latter is not possible around Kerr black holes. Moreover, we observe that the existence of several light rings around a horizon (several fundamental orbits, including a stable one), is a central ingredient for the existence of multiple shadows of a single hairy black hole. We also exhibit the lensing and shadows by Kerr black holes with scalar hair, observed away from the equatorial plane, obtained with PYHOLE.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.3 (Shadows of single black holes)

W G Cook, U Sperhake arXiv:1609.01292 [gr-qc] Class.Quant.Grav. 34 (2017) 035010 (D4.1), (D4.3)

Extraction of gravitational-wave energy in higher dimensional numerical relativity using the Weyl tensor
Gravitational waves are one of the most important diagnostic tools in the analysis of strong-gravity dynamics and have been turned into an observational channel with LIGO's detection of GW150914. Aside from their importance in astrophysics, black holes and compact matter distributions have also assumed a central role in many other branches of physics. These applications often involve spacetimes with D > 4 dimensions where the calculation of gravitational waves is more involved than in the four dimensional case, but has now become possible thanks to substantial progress in the theoretical study of general relativity in D > 4. Here, we develop a numerical implementation of the formalism by Godazgar and Reall [1] -- based on projections of the Weyl tensor analogous to the Newman–Penrose scalars -- that allows for the calculation of gravitational waves in higher dimensional spacetimes with rotational symmetry. We apply and test this method in black-hole head-on collisions from rest in D = 6 spacetime dimensions and find that a fraction (8.19 ± 0.05) × 10⁻⁴ of the Arnowitt–Deser–Misner mass is radiated away from the system, in excellent agreement with literature results based on the Kodama–Ishibashi perturbation technique. The method presented here complements the perturbative approach by automatically including contributions from all multipoles rather than computing the energy content of individual multipoles.
Deliverable D4.1 (Wave extraction in axisymmetry)
Deliverable D4.3 (Wave extraction, initial data)

J L Blázquez-Salcedo et al arXiv:1609.01286 [gr-qc] Phys.Rev.D 94 (2016) 104024 (D3.3)

Z Cao, A Cárdenas-Avendaño, M Zhou, C Bambi, C A R Herdeiro, E Radu arXiv:1609.00901 [gr-qc] JCAP 1610 (2016) 003 (D2.1)

V Cardoso, S Hopper, C F B Macedo, C Palenzuela, P Pani arXiv:1608.08637 [gr-qc] Phys.Rev.D 94 (2016) 084031 (D1.2), (D2.1)

Echoes of ECOs: gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon
Gravitational waves from binary coalescences provide one of the cleanest signatures of the nature of compact objects. It has been recently argued that the post-merger ringdown waveform of exotic ultracompact objects is initially identical to that of a black-hole, and that putative corrections at the horizon scale will appear as secondary pulses after the main burst of radiation. Here we extend this analysis in three important directions: (i) we show that this result applies to a large class of exotic compact objects with a photon sphere for generic orbits in the test-particle limit; (ii) we investigate the late-time ringdown in more detail, showing that it is universally characterized by a modulated and distorted train of "echoes" of the modes of vibration associated with the photon sphere; (iii) we study for the first time equal-mass, head-on collisions of two ultracompact boson stars and compare their gravitational-wave signal to that produced by a pair of black-holes. If the initial objects are compact enough as to mimic a binary black-hole collision up to the merger, the final object exceeds the maximum mass for boson stars and collapses to a black-hole. This suggests that -- in some configurations -- the coalescence of compact boson stars might be almost indistinguishable from that of black-holes. On the other hand, generic configurations display peculiar signatures that can be searched for in gravitational-wave data as smoking guns of exotic compact objects.
Deliverable D1.2 (Structure of stars with dark cores)
Deliverable D2.1 (Black holes with scalar fields)

J F M Delgado, C A R Herdeiro, E Radu, H Runarsson arXiv:1608.00631 [gr-qc] Phys.Lett.B 761 (2016) 234-241 (D2.1)

D Anderson, N Yunes, E Barausse arXiv:1607.08888 [gr-qc] Phys.Rev.D 94 (2016) 104064 (D3.2)

N Sanchis-Gual, J C Degollado, C Herdeiro, J A Font, P J Montero arXiv:1607.06304 [gr-qc] Phys.Rev.D 94 (2016) 044061 (D2.1)

V Cardoso, L Gualtieri arXiv:1607.03133 [gr-qc] Class.Quantum Grav. 33 (2016) 174001 (D1.3)

K Belczynski et al arXiv:1607.03116 [astro-ph] Astron.&Astrophys. 594 (2016) A97 (D3.1), (D3.2)

V Cardoso, A Coutant, M Richartz, S Weinfurtner arXiv:1607.01378 [astro-ph] Phys.Rev.Lett. 117 (2016) 271101 (D?.?)

A Nishizawa, A Sesana, E Berti, A Klein arXiv:1606.09295 [astro-ph] MNRAS 465 (2017) 4375-4380 (D3.2)

J F M Delgado, C A R Herdeiro, E Radu arXiv:1606.07900 [astro-ph] Phys.Rev.D 94 (2016) 024006 (D2.1), (D2.2)

Violations of the Kerr and Reissner-Nordström bounds: Horizon versus asymptotic quantities
A central feature of the most elementary rotating black hole (BH) solution in general relativity is the Kerr bound which, for vacuum Kerr BHs, can be expressed either in terms of the Arnowitt-Deser-Misner (ADM) or horizon “charges.” However, this bound is not a fundamental property of general relativity and stationary, asymptotically flat, and regular (on and outside an event horizon) BHs are known to violate the Kerr bound, in terms of both their ADM and horizon quantities. Examples include the recently discovered Kerr BHs with scalar [C. A. R. Herdeiro and E. Radu, Phys. Rev. Lett. 112, 221101 (2014)] or Proca hair [C. Herdeiro, E. Radu, and H. Runarsson, arXiv:1603.02687]. Here, we point out the fact that the Kerr bound in terms of horizon quantities is also violated by well-known rotating and charged solutions which are known in closed form, such as the Kerr-Newman and Kerr-Sen BHs. Moreover, for the former we observe that the Reissner-Nordström (RN) bound is also violated in terms of horizon quantities, even in the static (i.e., RN) limit. By contrast, for the latter the existence of charged matter outside the horizon allows for a curious invariance of the charge-to-mass ratio between the ADM and horizon quantities. Regardless of the Kerr bound violation, we show that in all cases the event horizon linear velocity [C. A. R. Herdeiro and E. Radu, Int. J. Mod. Phys. D 24, 1544022 (2015)] never exceeds the speed of light. Finally, we suggest a new type of informative parametrization for BH spacetimes where part of the asymptotic charge is supported outside the horizon.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.2 (Black holes with gauge fields)

K Glampedakis, G Pappas, H O Silva, E Berti arXiv:1606.05106 [astro-ph] Phys.Rev.D 94 (2016) 044030 (D3.3)

Y Ni, M Zhou, A Cárdenas-Arvendaño, C Bambi, C A R Herdeiro, E Radu arXiv:1606.04654 [astro-ph] JCAP 1607 (2016) 049 (D2.1), (D2.3)

F H Vincent, E Gourgoulhon, C Herdeiro, E Radu arXiv:1606.04246 [astro-ph] Phys.Rev.D 94 (2016) 084045 (D2.1), (D2.3)

Astrophysical imaging of Kerr black holes with scalar hair
We address the astrophysical imaging of a family of deformed Kerr black holes (BHs). These are stationary, asymptotically flat black hole (BH) spacetimes, that are solutions of General Relativity minimally coupled to a massive, complex scalar field: Kerr BHs with scalar hair (KBHsSH). Such BHs bifurcate from the vacuum Kerr solution and can be regarded as a horizon within a rotating boson star. In a recent letter, it was shown that KBHsSH can exhibit very distinct shadows from the ones of their vacuum counterparts. The setup therein, however, considered the light source to be a celestial sphere sufficiently far away from the BH. Here, we analyse KBHsSH surrounded by an emitting torus of matter, simulating a more realistic astrophysical environment, and study the corresponding lensing of light as seen by a very far away observer, to appropriately model ground-based observations of Sgr A*. We find that the differences in imaging between KBHsSH and comparable vacuum Kerr BHs remain, albeit less dramatic than those observed for the corresponding shadows in the previous setup. In particular, we highlight two observables that might allow differentiating KBHsSH and Kerr BHs. The first is the angular size of the photon ring (in a Kerr spacetime) or lensing ring (in a KBHSH spacetime), the latter being significantly smaller for sufficiently non-Kerr-like spacetimes. The second is the existence of an edge in the intensity distribution (the photon ring in Kerr spacetime). This edge can disappear for very non-Kerr-like KBHsSH. It is plausible, therefore, that sufficiently precise Very Long Baseline Interferometric observations of BH candidates can constrain this model.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.3 (Shadows of single black holes)

D Gerosa, C J Moore arXiv:1606.04226 [astro-ph] Phys.Rev.Lett. 117 (2016) 011101 (D3.1)

C A R Herdeiro, E Radu arXiv:1606.02302 [astro-ph] Phys.Rev.Lett. 117 (2016) 221102 (D2.2)

E Berti et al arXiv:1605.09286 [astro-ph] Phys.Rev.Lett. 117 (2016) 101102 (D3.2)

Y Brihaye, C Herdeiro, E Radu arXiv:1605.08901 [astro-ph] Phys.Lett.B 760 (2016) 279-287 (D2.1), (D2.2)

P V P Cunha, C A R Herdeiro, E Radu, H F Runarsson arXiv:1605.08293 [astro-ph] Int.Jour.Mod.Phys.D 25 (2016) 1641021 (D2.1), (D2.3)

F Hofmann, E Barausse, L Rezzolla arXiv:1605.01938 [astro-ph] Astrophys.J 825 (2016) L19 (D3.1)

A Nishizawa, E Berti, A Klein, A Sesana arXiv:1605.01341 [gr-qc] Phys.Rev.D 94 (2016) 064020 (D3.2)

D Gerosa, M Kesden arXiv:1605.01067 [astro-ph] Phys.Rev.D 93 (2016) 124066 (D3.1)

M Bastero-Gil, A Berera, R O Ramos, J G Rosa arXiv:1604.08838 [hep-ph] Phys.Rev.Lett. 117 (2016) 151301 (D1.1), (D1.4)

M Bonetti, F Haardt, A Sesana, E Barausse arXiv:1604.08770 [astro-ph] MNRAS 461 (2016) 4419-4434 (D3.2)

Post-Newtonian Evolution of Massive Black Hole Triplets in Galactic Nuclei: I. Numerical Implementation and Tests
Massive black-hole binaries (MBHBs) are thought to be the main source of gravitational waves (GWs) in the low-frequency domain surveyed by ongoing and forthcoming Pulsar Timing Array campaigns and future space-borne missions, such as eLISA. However, many low-redshift MBHBs in realistic astrophysical environments may not reach separations small enough to allow significant GW emission, but rather stall on (sub)pc-scale orbits. This "last-parsec problem" can be eased by the appearance of a third massive black hole (MBH) -- the "intruder" -- whose action can force, under certain conditions, the inner MBHB on a very eccentric orbit, hence allowing intense GW emission eventually leading to coalescence. A detailed assessment of the process, ultimately driven by the induced Kozai-Lidov oscillations of the MBHB orbit, requires a general relativistic treatment and the inclusion of external factors, such as the Newtonian precession of the intruder orbit in the galactic potential and its hardening by scattering off background stars. In order to tackle this problem, we developed a three-body Post-Newtonian (PN) code framed in a realistic galactic potential, including both non-dissipative 1PN and 2PN terms, and dissipative terms such as 2.5PN effects, orbital hardening of the outer binary, and the effect of the dynamical friction on the early stages of the intruder dynamics. In this first paper of a series devoted at studing the dynamics of MBH triplets from a cosmological perspective, we describe, test and validate our code.
Deliverable D3.2 (Astrophysical Observables)

V Cardoso, C F B Macedo, P Pani, V Ferrari arXiv:1604.07845 [astro-ph] JCAP 1605 (2016) 054 (D1.3), (D2.2)

C A R Herdeiro, E Radu, H F Rúnarsson arXiv:1604.06202 [gr-qc] Int.Jour.Mod.Phys.D 25 (2016) 1641014 (D2.1)

O Bertolami, C Cosme, J G Rosa arXiv:1603.06242 [hep-th] Phys.Lett.B 759 (2016) 1-8 (D1.4)

E Berti, V Cardoso, L C B Crispino, L Gualtieri, C Herdeiro, U Sperhake arXiv:1603.06146 [gr-qc] Int.Jour.Mod.Phys.D 25 (2016) 1641022 (D1.1)

T Hartwig, M Volonteri, V Bromm, R S Klessen, E Barausse, M Magg, A Stacy arXiv:1603.05655 [astro-ph] MNRAS 460 (2016) L74-L78 (D3.2)

A Maselli, H O Silva, M Minamitsuji, E Berti arXiv:1603.04876 [gr-qc] Phys.Rev.D 93 (2016) 124056 (D3.3)

E Barausse, N Yunes, K Chamberlain arXiv:1603.04075 [gr-qc] Phys.Rev.Lett. 116 (2016) 241104 (D1.3), (D3.1), (D3.3)

C Herdeiro, E Radu, H Rúnarsson arXiv:1603.02687 [gr-qc] Class.Quant.Grav. 33 (2016) 154001 (D.2.2)

Kerr black holes with Proca hair
Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we show this model admits asymptotically flat, stationary, axi-symmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in arXiv:1403.2757, that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the non-linear level. We confirm this expectation and explicitly construct examples of such Kerr black holes with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families with three continuous parameters (ADM mass, ADM angular momentum and Noether charge). They branch off from the Kerr solutions that can support stationary Proca clouds and reduce to Proca stars when the horizon size vanishes. We present the domain of existence of one family of KBHsPH, as well as its phase space in terms of ADM quantities. Some physical properties of the solutions are discussed; in particular, and in contrast with Kerr BHs with scalar hair, some spacetime regions can be counter-rotating with respect to the horizon. We further establish a no-Proca-hair theorem for static, spherically symmetric BHs but allowing the complex Proca field to have a harmonic time dependence, which shows BHs with Proca hair in this model require rotation and have no static limit. KBHsPH are also disconnected from Kerr-Newman BHs with a real, massless vector field.
Deliverable D2.2 (Black holes with gauge fields)

W Cook, P Figueras, M Kunesch, U Sperhake, S Tunyasuvunakool arXiv:1603.00362 [gr-qc] Int.Jour.Mod.Phys.D 25 (2016) 1641013 (D4.1), (D4.2)

V Cardoso, E Franzin, P Pani arXiv:1602.07309 [gr-qc] Phys.Rev.Lett. 116 (2016) 171101 (D3.1), (D3.2)

C Herdeiro, E Radu arXiv:1602.06990 [gr-qc] Phys.Lett.B 757 (2016) 268-274 (D2.2)

D Gerosa, U Sperhake, C D Ott arXiv:1602.06952 [gr-qc] Class.Quant.Grav. 33 (2016) 135002 (D2,1), (D3.2), (D3.3)

R Brito, V Cardoso, J V Rocha arXiv:1602.03535 [gr-qc] Phys.Rev.D 94 (2016) 024003 (D2.1) (D2.1)

V Cardoso, J V Rocha arXiv:1601.07552 [gr-qc] Phys.Rev.D 93 (2016) 084034 (D2.1)

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M Wang, C Herdeiro arXiv:1512.02262 [gr-qc] Phys.Rev.D 93 (2016) 064066 (D2.2)

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