# Phys482: General Relativity

Course 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% Homework sets, 30% Midterm, 40% Final Exam.

Course textbooks:

-- Sean Carroll, Spacetime and Geometry: An Introduction to General Relativity. Suitable for graduate and advanced undergraduate students.

-- Bernard Schutz, A First Course in General Relativity. For graduate and advanced undergraduate students.

Additional sources:

-- James Hartle, An Introduction to Einstein's General Relativity. A true undergrad book with many detailed calculations.

-- Hans Stephani, An Introduction to Special and General Relativity; an extensive book with clear and detailed explanations.

-- Wolfgang Rindler, Relativity; SPECIAL, GENERAL, AND COSMOLOGICAL;

a rigorous book but notationally unusual on occasion. For graduate and advanced undergraduates.

-- Leonard Susskind (and Andre Cabannes), General Relativity: The Theoretical Minimum; great read at all levels; not too technical, but includes enough math to capture Susskind’s clear insights.

• Steven Weinberg, Gravitation and Cosmology; an all-time classic with Weinberg’s useful insights that researchers and graduate students at all levels can benefit from. Could be excessive for undergrads, depending on their level.

• Charles W. Misner, John Archibald Wheeler, and Kip Thorne (MTW), Gravitation; another classic; this book is called the “Bible” of General Relativity. Could be overwhelming as a textbook but it is a must-have as an advanced side source.

Lecture notes:

Lecture 1: Introduction; equivalence principle, gravitational redshift, bending of light.

Lecture 2: Special Relativity review.

Lecture 3: Manifolds, vectors, 1-forms, and tensors in general.

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: Mercury's perihelion, Deflection of light, Schd black holes.

Lecture 10: Kruskal coordinates, Penrose diagrams, Star solutions.

Lecture 11: Rotating-Charged-BHs, BH-thermo, Cosmology-basics.

Lecture 12: Cosmology-cont, Inflation, CMB, early universe.

Lecture 13: Perturbation Theory and gravitational waves.

Sample homework sets:

The problems in the sets will be discussed in the recitation sessions by the TA of the course.

Sample exams: