**[Cr:4, Lc:3, Tt:1, Lb:0]**

Knowledge of content of **PHY301** and **PHY303** is essential to follow this course.

- Review of special relativity and Newtonian gravity.
- Equivalence principle, local inertial frames.
- The metric tensor. Measurements of lengths and synchronization of clocks.
- Coordinate transformations, manifolds and tensors.
- Christoffel symbols, geodesic equation, geodesic deviation equation and the curvature tensor.
- Stress-energy tensor, Bianchi identities, Einstein's equation.
- Maxwell's equations in curved space time, stress-energy tensor for the electromagnetic field.
- Synchronous coordinates.
- Gravitational field of a point mass, Schwarzschild metric and black holes. Orbits around a point mass, precession of perihelion, lensing equation. The horizon and the singularity in the Schwarzschild metric.
- Gravitational field of a star, interior and exterior solutions, gravitational field of a rotating body, Kerr metric.
- Post Newtonian (PN) and Post Minkowski (PM) description of theories of gravity.
- Experimental tests of the general theory of relativity.
- Linearized field equations, gauge freedom. scalar, tensor and vector modes.
- Gravitational waves. Observations of gravitational waves and their interpretation.
- Symmetries and Killing vectors.
- The cosmological principle, Robertson-Walker metric, Friedmann equations. Solutions of the Friedmann equations.
- Cosmological redshift, distances in cosmology. Observational constraints from distance measurement.
- Cosmic-Microwave Background Radiation (CMBR) in the standard cosmological model, flatness and horizon problems, inflationary scenarios.

- L. D. Landau & E. M. Lifshitz, Classical Theory of Fields, Butterworth-Heinemann (1980).
- C. W. Misner, K. S. Thorne & J. A. Wheeler, Gravitation, W. H. Freeman (1973).
- S. Weinberg,Gravitation and Cosmology, John Wiley & Sons (1972).
- T. Padmanabhan, Gravitation: Foundations and Frontiers, Cambridge University Press (2010).
- S. Weinberg, Cosmology, Oxford University Press (2008).
- J. B. Hartle, Gravity: An introduction to Einstein's General Relativity, Benjamin Cummings (2003).
- B. F. Schutz, A first course in general relativity, Cambridge University Press (2009).
- P. J. E. Peebles, Principles of Physical Cosmology, Princeton University Press (1993).
- T. Padmanabhan, Theoretical Astrophysics: Volume 3, Galaxies and Cosmology, Cambridge University Press (2002).
- S. Dodelson, Modern Cosmology, Academic Press (2003).