This is an elective course for advanced physics students with the appropriate background. Covers the principles of gravity theory based on Einstein’s general theory of relativity. Topics include: differential geometry, the principle of equivalence and Einstein’s field equation, the Schwarzschild solution, experimental tests, black holes, and gravitational waves.
Monday 11:00-13:00, Room 3
Thursday 11:00-13:00, Room 3
Geometric viewpoint on flat space physics, Special Relativity
Space-time interval, Lorentz transformations, Vectors and dual vectors (one-forms), Tensors
Riemannian geometry
Manifolds, The metric, Parallel transport and Christoffel symbols, Geodesics, Covariant differentiation, The curvature tensor
Gravity
The Einstein equation, The Equivalence Principle, The Newtonian limit, Gravitational redshift, Including matter: the energy-momentum tensor, The cosmological constant
Gravitational waves
Perturbation theory, Gauge transformations, The polarization of gravitational waves, Energy and momentum carried by waves, Detection of gravitational waves
The Schwarzschild solution
Derivation of the Schwarzschild metric, Birkhoff’s theorem, Geodesics of Schwarzschild, Experimental tests, Coordinate and curvature singularities
Black Holes
The Schwarzschild black hole, Killing and event horizons, Charges of spacetimes: mass, angular momentum, electric charge, The Vaidya metric
The main textbook of the course is:
- Carroll, Sean M., Spacetime and Geometry: An Introduction to General Relativity. Cambridge University Press, 2019.
More elementary textbooks include:
- Schutz, Bernard, A First Course in General Relativity. 2nd Edition. Cambridge University Press, 2009
- Hartle, James B., Gravity: An Introduction to Einstein’s General Relativity. Harlow: Pearson, 2003.
The definitive rigorous textbook is:
- Wald, Robert M., General Relativity. University of Chicago Press, 1984
The most comprehensive textbook is:
- Misner, Charles W., Thorne, K. S., & Wheeler, J. A. Gravitation. Princeton University Press, 2017
The most succinct textbook is:
- P. A.M. Dirac, General Theory of Relativity, Princeton University Press, 1996
