Dr Peter J O'Donnell FIMA

Career

  • 2012-present: Affiliated Lecturer, DAMTP
  • 2014-present: Fellow and Tutor, St. Edmund's College
  • 2009-present: Director of Studies, St. Edmund's College
  • 2007-2009: Teaching Associate, Queens’ College

Research

  • Lanczos potential theory. The Weyl tensor can be generated differentially by a three index tensor: the Lanczos tensor, which was derived from a Lagrangian that was initially constructed to analyse the self-dual part of the Riemann tensor. An ongoing study is being carried out to investigate the mathematical and physical properties of the Lanczos tensor. In generating the Weyl tensor the Lanczos tensor acts as a potential – analogous to the electric tensor in electromagnetic theory.
  • Twistor theory applied to Lanczos potential theory. The purpose of this research is to utilise the techniques of twistor theory in order to carry out a qualitative and quantitative analysis of the Lanczos potential, which appears to have some connection with local twistor transport.
  • The concept of infinity applied to science, the arts and theology. The purpose of this research is to ascertain the relevance and possible connections in the aforementioned areas.

Selected Publications

  • On a new approach of deriving the Weyl-Lanczos equations giving rise to a physical interpretation to the Lagrange multiplier q, Eur. Phys. J. Plus. 126: 87. DOI: 10.1140/epjp/i2011-11087-7 (2011)
  • A brief historical review of the important developments in Lanczos potential theory, EJTP. Vol 7, No. 24, (2010) (with H. Pye)
  • Lanczos potential for conformally flat space-times II, Rel. Grav. Cos. Vol. 3, no. 3, (2009)
  • A solution of the Weyl-Lanczos equations for a type N space-time, Icfai. J. Phys. Vol. 1, no.3, (2008)(with A. Roberts)
  • Conformal transformations of the Lanczos potential, Rel. Grav. Cos. Vol. 2, no. 2, (2005)
  • On a new curvature quantity in general relativity, (Bad Honnef. Conf. Proc.) (2005)
  • Lanczos potential for conformally flat space-times, Il Nuovo Cimento B, vol. 119, no. 4, (2004)
  • A method for finding Lanczos coefficients with the aid of symmetries, C. J. Phys. Vol. 54, no. 9, (2004)
  • A solution of the Weyl-Lanczos equations for the Schwarzschild space-time, Gen. Rel. Grav. vol. 36, no 6, (2004)

Books

  • Essential Dynamics & Relativity (Taylor and Francis/CRC Press, 2014)
  • Relativity, Gravitation, Cosmology: New Developments (Editor) (Nova Science, 2006)
  • Introduction to 2-Spinors in General Relativity (World Scientific, 2003)
  • The Art and Science of Infinity (in preparation)

Lecturing

  • Part IA Course: Mechanics (Michaelmas Term).
  • Graduate Course: 2-Spinors in General Relativity (Lent Term)
  • Part IA Course: Mathematical Methods III (NST) (Easter Term).