PH6002: General Relativity

L-T-P-C: 3-0-0-3

Prerequisites: PH5001 , PH 5003

Syllabus

Module 1: Special relativity

( Lecture hours: 7 , Tutorial hours: 0 , Lab hours: 0 )

Principle of relativity and electrodynamics, postulates of special relativity, Invariance of interval, Lorentz transformations, simultaneity in special relativity, Four-vectors and tensors, Action for the relativistic free particle, conservation of four-momentum, Action for charged particles, Maxwell's equations in covariant form .

Module 2: Towards general relativity

( Lecture hours: 5 , Tutorial hours: 0 , Lab hours: 0 )

Action at a distance, gravity as geometry, The equivalence principle, Dealing with geometry: curvilinear coordinates, Covariant and contravariant tensors .

Module 3: Formalization: manifolds and differential geometry

( Lecture hours: 8 , Tutorial hours: 0 , Lab hours: 0 )

Manifolds, calculus on manifolds: functions, curves, vectors and one-forms, tensors, Differential geometry: metric, covariant derivative, affine connection, Integration on manifolds .

Module 4: Motion of test particles in curved spacetime

( Lecture hours: 8 , Tutorial hours: 0 , Lab hours: 0 )

Action for a free particle in curved spacetime, geodesic equation, local inertial frames, Isometries: the Killing equation and conserved quantities, Geometry outside the star: Schwarzschild solution, symmetries and conserved quantities, Motion of particles in the Schwarzschild metric: gravitational redshift, precession of the perihelion, bending of light .

Module 5: Einstein equations

( Lecture hours: 10 , Tutorial hours: 0 , Lab hours: 0 )

Riemann tensor, geodesic deviation, curvature, Action for the gravitational field, Einstein equations, Stress-energy tensor: perfect fluid, scalar and electromagnetic field .

Module 6: Term paper presentations

( Lecture hours: 4 , Tutorial hours: 0 , Lab hours: 0 )

Student term paper presentations; possible topics include the Friedmann-Robertson-Walker (FRW) metric, gravitational waves, verifying the Schwarzschild solution, black holes, etc. .

Study Materials

Textbooks

  1. Spacetime and Geometry, S. Carroll, Pearson India (2016), ISBN: 978-9332571655
  2. Gravity: An Introduction to Einstein's General Relativity, J. B. Hartle, Pearson Education (2014), ISBN: 9332535086
  3. General Relativity: An Introduction for Physicists, M. P. Hobson, Cambridge University Press (2006), ISBN: 0521829518

References

  1. The Classical Theory of Fields (Course of Theoretical Physics, Volume 2), L. D. Landau and E. M. Lifshitz, 4th Edition, CBS Publishers, ISBN: 9788181477873
  2. General Relativity, R. M. Wald, The University of Chicago Press (1984), ISBN: 8188689270
  3. A First Course in General Relativity, B. F. Schutz, Cambridge University Press (1990), ISBN: 1107696690
  4. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, S. Weinberg, Wiley, ISBN: 978-8126517558