Venue: Chern Lecture Hall

Class Timings: 12:00 PM - 1:30 PM, Tuesdays, Wednesday and Thursdays

First Meeting: 17th January 2023

Course Description:

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 Evaluation: 30% Home work, 30% Mid-term, 40% Final

Credit Score: 4