General Relativity

Course Outcome:

Course Syllabus:

Unit I:
Review of Lorentz transformations and special theory of relativity.

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.

Unit II:

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.

Einsteins equation, Lagrangian formulation, Einstein-Hilbert action.

Unit III:

Schwarzschild solution: construction of the metric and its symmetries; motion of a particle in the Schwarzschild metric; Schwarzschild black hole; white holes and Kruskal extension of the 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.

Unit IV:

Precession of the perihelion; bending of light; radar echo delay.

Linearised theory, gravitational waves, field far from a source, energy in gravitational waves, quadrupole formula

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 implications.

Text book:

1. A Relativist’s toolkit, by Eric Poisson, Cambridge University Press 

2. Gravitation and Cosmology, by Steven Weinberg, Wiley

3. Introduction to General Relativity, by Lewis Ryder, Cambridge University Press

4. A first course in general relativity, by Bernard F Schutz, Cambridge University Press

5. General Relativity: An Introduction for Physicists, by M P Hobson, G P Efstathiou, A N Lasenby, Cambridge University Press

6. Gravitation: Foundations and Frontiers, by T Padmanabhan, Cambridge University Press

Reference book:

1. General Relativity, by Robert Wald, The University of Chicago Press
2. Gravitation, by C W Misner, K S Thorne, J A Wheeler, Princeton University Press

3.Gravity: An introduction to Einstein’s General Relativity, by James B Hartle, Pearson Education

4.Relativity, by Wolfgang Rindler, OUP Oxford

5.Semi-Riemannian Geometry, by Barrett O’Neill, Elsevier

6.Spacetime and Geometry: An introduction to General Relativity, by Sean M Carroll, Cambridge University Press

7.Exploring Black Holes, by Edwin F Taylor, John Archibald Wheeler, Addison Wesley Longman

8.General Relativity, by Norbert Straumann, Springer Berlin Heidelberg

9.The Mathematical Theory of Black Holes, by S Chandrasekhar, Clarendon Press