Math 6110 Advanced gereral relativity


Advanced General Relativity is a second course exploring the geometrical structure and physical content of Einstein’s theory of gravity. Topics covered will include the geometry of vector bundles, congruences of geodesics, intrinsic and extrinsic geometry of hypersurfaces and the Lagrangian and Hamiltonian formulation of general relativity. These ideas will then be applied to the initial value problem for general relativity, spacetime surgery, the definition of mass and angular momentum for gravitational fields, the characterization of black hole horizons, black hole mechanics, and studies of important solutions to the Einstein equations in four and higher dimensions.


A background in introductory general relativity equivalent to our M6130 and a working knowledge of differential geometry equivalent to our M4230.

Possible texts

  • A Relativist’s Toolkit: the mathematics of black hole mechanics, Eric Poisson (this is the one we usually use)
  • General Relativity, Robert Wald