Course info

• Tensors and their transformation laws; Christoffel symbol and Riemann tensor; geodesics; parallel transport along open lines and closed curves; general properties of the Riemann tensor. 
• Equivalence principle and its applications: gravity as a curvature of space-time; geodesics as trajectories under the influence of gravitational field; generalisation to massless particles; gravitational red-shift; motion of a charged particle in curved space-time in the presence of an electric field; Maxwells equation in curved space-time. 
• Einstein's equation, Schwarzschild solution: construction of the metric and its symmetries; Motion of a particle in the Schwarzschild metric; precession of the perihelion; bending of light; Horizon, its properties and significance. 
• Lagrangian formulation of general relativity, Einstein-Hilbert action. 
• Tetrad formulation and coupling to spinors. Linearised theory, gravitational waves, energy in gravitational waves. 
• Elementary cosmology: principles of homogeneity and isotropy; Friedman-Robertson-Walker metric; open, closed and flat universes; Friedman equation and stress tensor conservation, equation of state, big bang hypothesis and its successes.

Course Outcome:

• Apply methods of tensor analyses to problems of physics and mathematics. 
• Become familiar with the physical basis of Einstein’s relativistic theory of gravitation, i.e. General Relativity and its implications. 
• Be trained in techniques used in applications of general relativity to problems of relativistic astrophysics and cosmology.  Work on exciting frontier areas of astrophysical relativity like gravitational waves, gravitational lensing, black holes and neutron stars. 
• Proceed to advanced topics in general relativity and its applications to string theory