Disclaimer

The primary purpose of these html notes is to allow screen reading software to convert equations into synthesised speech. This should (hopefully) work. I have made no effort to make the equations look pretty and while they appear nicely on some browsers, they fail to render correctly on others. If you're not using speech conversion software then you will likely be better served by the lecture notes in pdf form.

Conventions

We use the metric with signature $(-+++)$. This is the opposite convention to my lecture notes on Special Relativity and Quantum Field Theory, but it does agree with the lecture notes on Cosmology and on String Theory. There is some mild logic behind this choice. When thinking about geometry, the choice $(-+++)$ is preferable as it ensures that spatial distances are positive; when thinking about quantum physics, the choice $(+---)$ is preferable as it ensures that frequencies and energies are positive. Ultimately you just need to get used to both conventions.

When dealing with physics, spacetime indices are greek $\mu ,\nu =0,1,2,3$, spatial indices are roman $i,j=1,2,3$.

• 0 Introduction

• 1 Geodesics in Spacetime

• 2 Introducing Differential Geometry

• 3 Introducing Riemannian Geometry

• 4 The Einstein Equations

• 5 When Gravity is Weak

• 6 Black Holes