Numerical relativity is the art of constructing spacetimes by solving the Einstein equations numerically on a computer. There is often no other way of simulating compact objects such as black holes and neutron stars, and their gravitational wave emission.

Mathematical General Relativity uses methods from differentialgeometry, topology and analysis to study the structure of spacetime. Singularities form the boundaries of spacetime, but can also be seen as physical objects.

These relics of dead stars are the most compact objects in theuniverse. General relativity plays a key role in their dynamics. They are the main sources of gravitational waves. Their gravitational potential energy also powers photon and neutrino emission in the most violent and luminous astrophysical events.

Follow this link for a sample of possible PhD projects.