Theory of General Relativity

This course is taught at Leiden University.
Lecturer: Prof.dr. A. Achúcarro (achucar@lorentz.leidenuniv.nl)

The classical theory of gravity can be interpreted as the geometry of space-time.It combines the language of field theory with the language of differential geometry on manifolds. The basic concepts of these subjects will be introduced and it will be shown how they are used to describe gravitational phenomena, from relativistic corrections to orbits of planets and stars, to gravitational waves, black holes and the evolution of the universe at large.

Topics:

• Equivalence principle, geodesic motion;

• Differential geometry on manifolds, including the concepts of metric, connection and curvature;

• Symmetries and Killing vectores;

• Einstein equations, variational principle;

• Schwarzschild solution, stars and black holes;

• Cosmology of a homogeneous and isotropic universe;

• Gravitational waves.