Physics 786: General Relativity and Cosmology
Fall, 2018

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.

Development of general relativity

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

Consequences of general relativity

• Bending of light
• Orbital precession
• 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
• Quantum gravity - Hamiltonian constraint, Wheeler-DeWitt equation, survey of modern approaches

Course requirements and grade:

• Problem sets (80%)
• Final project (20%)

Reading material:

• Text:  There is no required textbook. The instructor's notes will be made available at the course website following 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

Lecture Notes will be posted here:
                       

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 23
Lecture Notes 5		Lecture Notes 15		Lecture Notes 23.5
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 will generally be posted here Wednesdays and due the following Wednesday.
Problem Set 1 (pdf), due Wednesday, September 12. Will be collected in class following Hurricane Florence.   Solutions
Problem Set 2 (pdf), due in the second class following Hurricane Florence.   Solutions
Problem Set 3 (pdf), due Wednesday, September 26. Solutions
Problem Set 4 (pdf), due Wednesday, October 3.    Solutions
Problem Set 5 (pdf), due Wednesday, October 10.    Solutions
Problem Set 6 (pdf), due Wednesday, October 24.    Solutions
Problem Set 7 (pdf), due Wednesday,October 31.    Solutions
Problem Set 8 (pdf), due Wednesday, November 7.    Solutions
Problem Set 9 (pdf), due Monday, November 19.    Solutions
Problem Set 10 (pdf), due Monday, December 3.    Solutions

Supplementary Material
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.
Tensors: a guide for undergraduate students
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.
Daniel Baumann's TASI Lectures on Inflation.
Martin Bauer and Tilman Plehn's Yet another introduction to dark matter. Pardon the coffee stain.
Simon Ross's notes on black hole thermodynamics.
Carlo Rovelli's Notes for a brief history of quantum gravity.
Bryce DeWitt's Quantum Theory of Gravity. I. The Canonical Theory