Physics 786: General Relativity and Cosmology
Fall, 2020

Office hours: Whenever you have a question about the course material, feel free to email to set up a remote Zoom meeting.
Course website: http://physics.wm.edu/~erlich/786F20

Instructor: Josh Erlich, Small Hall 332B, 757-221-3763, erlich@physics.wm.edu
Note that I will likely be home most days this semester due to the pandemic.

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 video introduction

Development of general relativity

• The meaning of inertia
• Newtonian gravity
• The equivalence principle(s)
• Gravitation as a field theory
• Gravitation as geometry

Tests of general relativity

• Bending of light
• Orbital precession
• Gravitational redshift
• Shapiro time delay

Applications of general relativity

• Gravitational radiation
• Black holes
• Stars - neutron stars, white dwarfs, Chandrasekhar limit
• Cosmology - big bang, Friedmann-Robertson-Walker cosmology, inflation

If spacetime allows

• Quantum field theory in curved spacetime, black hole thermodynamics
• Quantum gravity - Hamiltonian constraint, Wheeler-DeWitt equation, survey of modern approaches
• Puzzles of relativity - Problem of time, the hole argument, diffeomorphism-invariant observables

Course requirements and grade:

• Problem sets (70%)
• Paper (15%)
• Presentation (15%)
• A 92-100. A- 88-91, B+ 84-87, B 80-83, B- 75-79, C+ 71-74, C 67-70, C- 62-66, D+ 58-81, D 54-57, D- 50-53, F <50

Reading material:

• Text:  There is no required textbook. The instructor's notes will be made available at the course website with each class. The official recommended texts are Weinberg's book and the Feynman lectures, both excellent references despite their age, with insights that make those books unique.

• Recommended texts:
  • S. Weinberg, Gravitation and Cosmology
  • R. Feynman, F. Morinigo, W. Wagner, Feynman Lectures on Gravitation
  • S. Carroll, Spacetime and Geometry
  • R. Wald, General Relativity
  • A. Zee, Einstein Gravity in a Nutshell
  • L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields
  • S. Dodelson, Modern Cosmology

Lecture Notes
              

Lecture Notes 1		Lecture Notes 11		Lecture Notes 21
Lecture Notes 2		Lecture Notes 12		Lecture Notes 22
Lecture Notes 3		Lecture Notes 13		Lecture Notes 22.5
Lecture Notes 4		Lecture Notes 14
Lecture Notes 5		Lecture Notes 15
Lecture Notes 6		Lecture Notes 16
Lecture Notes 7		Lecture Notes 17
Lecture Notes 8		Lecture Notes 18
Lecture Notes 9		Lecture Notes 19
Lecture Notes 10		Lecture Notes 19.5
		Lecture Notes 20

Problem Sets
Problem Set 1, due Wednesday, September 9.
Problem Set 2, due Wednesday, September 16.
Problem Set 3, due Wednesday, September 23.
Problem Set 4, due Wednesday, September 30.
Problem Set 5, due Wednesday, October 7.
Problem Set 6, due Wednesday, October 14.
Problem Set 7, due Wednesday, October 21.
Problem Set 8, due Monday, November 2.
Problem Set 9, due Wednesday, November 11.

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.
Daniel Baumann's TASI Lectures on Inflation.
Martin Bauer and Tilman Plehn's Yet another introduction to dark matter. Pardon the coffee stain.