Syllabus
More on geometry: Lie derivative and space-time symmetries, tensor densities, covariant divergence, Fermi-Walker transport.
Invariant and coordinate features of the Schwarzschild solution, analytic extension of the metric.
Pericentre precession and light bending in the Schwarzschild field.
Reissner-Nordström solution of the Einstein equations.
Kerr and Kerr-Newman solutions of the Einstein equations, Carter equations for electro-geodesic test motion.
Gravitational collapse and black holes: black-hole uniqueness theorems, formation of black holes, laws of black-hole (thermo)dynamics, extraction of energy from black holes.
Relativistic theory of stellar equilibria: description of a static and spherically symmetric star, equations of stellar equilibria, radial oscillations and stability.
Final stages of stellar evolution: degenerate fermion gas, white dwarfs and neutron stars; Chandrasekhar limit.
Linearized theory of gravitation, plane gravitational waves, wavefronts, exact plane wave.
Annotation
Tensor analysis. Curvature and Einstein gravitational law. Schwarzschild solution of Einstein equations. Black holes and gravitational collapse. Astrophysics of black holes. General relativity in other branches of physics.
Linearised theory of gravitation, gravitational waves. For the 1st year of the TF, MOD and AA studies. Knowledge of general relativity is presumed on the level of TMF111 lecture.