Unit 1

Tensor Calculus and Differential Geometry: Riemannian space, Curvilinear coordinates, Tensors, Affine connection, Covariant derivative, Geodesics, Riemann-Christoffel curvature tensor, Bianchi identities, Ricci Tensor, Curvature Scalar.

Unit 2

Special Theory of Relativity and Introduction to Gravity: Minkowski spacetime, Special Theory of Relativity, Relativistic Dynamics. The principle of equivalence, Principle of General covariance, General Theory of Relativity – historical developments.

Unit 3

Einstein Field Equations: Gravity and Geometry, Energy-momentum tensor, Curvature tensors, Bianchi identities, Einsten tensor, Field equation, Weak Gravitational Field.

Unit 4

Schwartzchild Solution: Centrally symmetric Gravitational Field, Static spherically symmetric space-time, Schwartzchild Solutions
Black Holes: Relativistic Stellar star structure, Gravitational Collapse, Black Holes

Prerequisites: Mathematical Physics & Special Theory of Relativity
Objectives: To have a physical idea and mathematical understanding of General theory of Relativity and its applications

Text Books

1. Steven Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley India, 2008.
2. Øyvind Grøn, Sigbjorn Hervik, Einstein’s general theory of relativity: with modern applications in cosmology, 2002.
3. Ashok Das, Lectures on Gravitation, World Scientific, 2013.

Reference Books

1. Landau & Lifshitz, Classical Field Theory, University Science Books, 1E, 2004.
2. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, Princeton Univ Press
3. A. Einstein, Relativity: The Special and the General Theory