Topics: Special Relativity review, manifolds, tensors, differential forms, curvature, parallel transport, geodesics, Riemann tensor, geodesic deviation, Einstein’s equations, Lagrangian formulation of GR, Schwarzschild solutions, black holes, Penrose diagrams, FRW cosmology, perturbation theory, gravitational waves.
Grading: 30% Midterm I, 30% Midterm II, 40% Final Exam.
Textbooks:
-- Sean Carroll, Spacetime and Geometry: An Introduction to General Relativity, Pearson Education Limited, 2014.
-- Bernard Schutz, A First Course in General Relativity, Cambridge University Press, 2009.
Additional sources:
-- James Hartle, An Introduction to Einstein's General Relativity, Pearson Education Limited, 2014.
-- Hans Stephani, An Introduction to Special and General Relativity, Cambridge University Press, 2004.
-- Wolfgang Rindler, Relativity: Special, General, and Cosmological, Oxford University Press, 2006.
-- Leonard Susskind (and Andre Cabannes), General Relativity: The Theoretical Minimum, Penguin Books, 2023.
-- Steven Weinberg, Gravitation and Cosmology, Wiley, 1972.
-- Charles W. Misner, John Archibald Wheeler, and Kip Thorne (MTW), Gravitation, W. H. Freeman and Company, 1973.
Lecture notes:
Lecture 1: Introduction; equivalence principle, gravitational redshift, bending of light.
Lecture 2: Special Relativity review.
Lecture 3: Manifolds. Tensors (scalar, vectors, 1-forms, and higher rank tensors).
Lecture 4: Locally inertial frames, tensor densities, covariant derivative, Christoffel symbols.
Lecture 5: Parallel transport, geodesic, curvature, Riemann tensor and its properties.
Lecture 6: Geodesic deviation, Ricci tensor, Ricci scalar, Killing vectors, and symmetries.
Lecture 7: Gravitation, Einstein equation, Lagrangian formulation of GR.
Lecture 8: Schd solution, its singularities, Killing vectors, and geodesics.
Lecture 9: Geodesics of Schd, experimental tests of GR, BHs.
Lecture 10: BHs, Kruskal coordinates, Penrose diagrams, Star solutions.
Lecture 11: Rotating-Charged-BHs, BH-thermo, Cosmology-basics.
Lecture 12: Cosmology (continue), inflation, CMB, early universe.
Lecture 13: Perturbation theory and gravitational waves.
Sample problem sets:
The problems in the sets will be discussed in the recitation sessions by the TA of the course.
Sample exams: