General Relativity

Objective of the course

This course will be helpful for students who are interested in high-energy physics and quantum gravity/string theory in future.
The pre-requisite for this course is mathematical methods I and II, classical mechanics and electrodynamics and special theory of relativity. Although this course requires a good knowledge of special theory of relativity (STR) however, whatever is required from STR, I shall discuss in the class.

Outline of the course

1. STR: Few basic and important concepts in special relativity.
2. Mathematical background : Mathematical aspects: tensor algebra, transformation of coordinates, covariant, contravariant tensors, tensor fields, Lie derivative, covariant derivative, affine connections, affine geodesic, Riemann tensor, metric, metric geodesic, metric connection, curvature tensor, variational method for geodesic.
3. Introduction to GR : Inertial frames, gravitational mass and inertial mass, equivalence principle: weak form, strong form, principle of general covariance.
4. Field equations in general relativity: geodesic deviation, vacuum Einstein equations.
5. Tests of GR : Perihelion shift or mercury, bending of light.
6. Action formulation of GTR.
7. Solution of Einstein equations: black holes - Schwarzschild black hole. Spacetime structure of Schwarzschild black hole.
8. Penrose diagram for Schwarzschild black holes.
9. Cosmology: FRW Universe.
10. Gravitational wave.

Lecture notes :

Coming soon

Home work

Useful links