Details of PH4205 (Spring 2017)

Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
PH4205 General Theory of Relativity and Cosmology Narayan Banerjee


  • Riemannian Geometry: Vectors and Tensors; parallel transport, covariant differentiation; Geodesics; Riemann-Christoffel curvature tensor - its symmetry properties, Ricci tensor; Bianchi identities; vanishing of the curvature tensor as a condition for flatness, Geodesic deviation equation.

  • Principle of general covariance and principle of equivalence; Einstein field equations, derivation from a variational principle.

  • Schwarzschild exterior solution, Birkhoff's theorem. Geodesics in a Schwarzschild geometry. Crucial tests of general relativity - perihelion shift, bending of light, gravitational redshift. Schwarzschild blackhole - event horizon and static limit, Kruskal - Szekere's diagram.

  • Maxwell's equations in general relativity. Reissner - Nrdstrm solutions - charged blackhole. Kerr - Newman solutions, Kerr - Newman blackholes. Ergosphere, Penrose process and extraction of energy from a blackhole.

  • Interior solutions for a spherical star; Oppenheimer - Volkoff equation; Chandrasekhar limit and white dwarfs, Oppenheimer - Volkoff limit and neutron stars; pulsars. Oppenheimer - Snydder non-static dust model - gravitational collapse.

  • Linearized filed equations and gravitational waves .

  • Lie derivatives; spacetime symmetries, Killing vectors.

  • Cosmological assumptions - Cosmological principle,Hydrodynamics approximation and general relativity; Robertson-Walker metric. Red shift, Hubble's observations. Friedman models, cosmological parameters, age of the Universe, cosmological horizons; models with $\Lambda$ - term.


  1. J. V. Narlikar, Lecture on General Relativity and Cosmology, The Macmillan Company of India Limited.

  2. R. Adler , M. Bazin and M. Schiffer, Introduction to General Relativity, McGraw-Hill.

  3. B. F. Schutz, A First Course in General Relativity, Cambridge University Press.

  4. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Freeman and Co. (1973).

  5. S. Caroll, Spacetime and geometry : an introduction to general relativity, Addison Wesley (2004).

  6. R. D'Inverno, Introducing Einstein's relativity, Oxford university press (2005).

  7. J. B. Hartle, Gravity : an introduction to Einstein's general relativity, Pearson education (2003).

  8. S. Weinberg, Gravitation and cosmology : principles and applications of the general theory of relativity, John wiley and Sons (2004).

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Elective
2 IP 4 Elective
3 IP 6 Not Allowed
4 MR 2 Elective
5 MR 4 Not Allowed
6 MS 8 Elective
7 RS 1 Elective
8 RS 2 Elective