Details of ID4208 (Spring 2013)
| Level: 4 | Type: Theory | Credits: 3.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| ID4208 | General Relativity and Cosmology | Narayan Banerjee |
| Syllabus |
|---|
| 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 ? - term. |
| References |
|---|
| 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. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Elective |
| 2 | IP | 4 | Elective |
| 3 | MS | 8 | Elective |
| 4 | RS | 1 | Elective |