**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

- Teacher: Ashoke Sen