Office hours:
Whenever you have a question about the course material, feel free to
stop by my office (Small 332B) or email to arrange a meeting..
Course website: http://physics.wm.edu/~erlich/786S23
Instructor: Josh Erlich, Small Hall 332B, 757-221-3763, erlich@physics.wm.edu
Prerequisites: Familiarity with classical mechanics and electromagnetism at the advanced undergraduate/intro graduate level will be assumed.
This is a course on Einstein's theory of gravitation and cosmology, including the classic tests and consequences of the theory. The course will compare the field-theoretic and geometric viewpoints of the subject, and time permitting will include an introduction to quantum fields in curved spacetime and discussion of the challenges facing quantum gravity.
Course requirements and grade:
Reading material:
Lecture Notes
Lecture Notes 1: Introduction, Newtonian Gravity, Inertia
Lecture Notes 2: Special Relativity, Lorentz Invariance, Tensors
Lecture Notes 3: Consequences of the Equivalence Principle, The Geodesic Equation
Lecture Notes 4: Dynamics for Gravity
Lecture Notes 5: Gravitational plane waves
Lecture Notes 6: Conservation of Energy-Momentum and the need for a nonlinear theory
Lecture Notes 7: Spacetime and Geometry
Lecture Notes 8: Tensors under general coordinate transformations
Lecture Notes 9: More geometry, Covariant Deriative, Covariant div, curl, Laplacian
Lecture Notes 10: Constant Vector Fields, Parallel Transport, Curvature
Lecture Notes 11: Einstein's Equations
Lecture Notes 12: The Schwarzschild Solution, Gravitational Energy
Lecture Notes 13: Coordinate Singularities and Curvature Singularities, Causal Structure of the Schwarzschild Black Hole
Lecture Notes 14: Killing vectors and constants of motion; Motion in Schwarzschild spacetime
Lecture Notes 15: Bending of Light, Precession of the Perihelion
Lecture Notes 16: Stars, Chandrasekhar limit
Lecture Notes 17: Gravitational Radiation, part 1
Lecture Notes 18: Gravitational Radiation, part 2
Lecture Notes 19: Geodesic deviation
Lecture Notes 20: Time-Dependent Spherically Symmetric Solutions to Einstein's Equations
Lecture Notes 21: The Expanding Universe
Lecture Notes 22: Sources of Cosmological Data
Lecture Notes 23: Puzzles and Cosmic Inflation
Lecture Notes 24: Einstein-Hilbert Action, Spin Connection
Lecture Notes 25*:Semiclassical Gravity, Hawking Radiation
Problem Sets
Problem sets will be posted here and will generally be due on Fridays.
Problem Set 1, due Friday, February 10.
Problem Set 2, due Friday, February 17.
Problem Set 3, due Friday, February 24.
Problem Set 4, due Friday, March 3.
Problem Set 5, due Friday, March 10.
Problem Set 6, due Friday, March 24.
Problem Set 7, due Friday, March 31.
Problem Set 8, due Friday, April 7.
Problem Set 9, due Friday, April 14.
Problem Set 10, due Friday, April 28.
Problem Set 11, due Friday, May 5.*
* Extensions on the final assignment and paper will be automatically granted until May 16 at 2pm.
Supplementary Material - Material will be added as we uncover new topics during the course.
Tensors: a guide for undergraduate students. Open access version here.
In case you are interested in the history of the covariant formulation of electrodynamics, I believe the earliest reference is this text by Minkowski, which is translated to English along with works by Einsten here.
Einstein's The Meaning of Relativity is available through Project Guttenberg here.
Deser's 1970 discussion of spin-2 fields vs GR is available reprinted here.
Deser's 2009 discussion of spin-2 fields vs GR is available here.
Padmanabhan's 2004 objections to this approach are presented here.