PHY 620 - General Relativity

PHY 620 - General Relativity

Professor: Marilena LoVerde
email: marilena.loverde {{ AT }}
Office: Math 6-103
Course Website:

Lectures: Wednesday and Friday 8:30AM - 9:50AM, Physics 127
Office Hours: Thursday 10:30-11:30AM, Math 6-103
Grading: 30% Homework, 30% Midterm, 40% Final Exam.

Course Topics: Flat spacetime and Special Relativity, intro to mathematical framework and basic differential geometry, gravity and Einstein's equation, Schwarzschild solution, black holes, conformal diagrams, cosmological solutions, gravitational waves and the weak field limit. Possible additional topics include cosmological perturbation theory, Hawking radiation, inflation and quantum fluctuations during inflation, astrophysical black holes and neutron stars.

Course Textbook: Sean Carroll's Spacetime and Geometry: An Introduction to General Relativity

Additional Recommended Texts: Bernard F. Schutz, A First Course in General Relativity (easy); Robert M. Wald, General Relativity (hard/more formal); Steven Weinberg Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (intermediate/more phenomenological); Misner, Thorne, and Wheeler, Gravitation (intermediate/excellent reference on specific topics, notation a bit nonstandard)

Learning Outcomes: Students who complete this course will have a basic understanding of differential geometry, a thorough understanding of special relativity, Einstein's equation, and several known solutions to Einstein's equation including black holes and solutions for the expanding universe. Understanding these topics will gives students foundations for research in theoretical physics and astrophysics.


Homework 1

Homework 1 Solutions

Homework 2

Homework 3

Homework 3 Solutions

Homework 4

Homework 4 Solutions

Last Year's Midterm
Last Year's Midterm problem 1
Last Year's Midterm problem 2
Last Year's Midterm problem 3

Homework 5

Homework 5 Solutions

Homework 6

Homework 6 Solutions

Homework 7

Homework 7 Solutions

Homework 8

Homework 8 Solutions


LIGO paper accompanying the final

Useful Things

A helpful discussion of the ``special relativity on a torus" problem in Homework 1 can be found in this paper by Weeks . A key feature of this universe is that there is a preferred observer who sees the matching condition for the torus to be simultaneous. Observers at rest in that frame see images of themself (in the past) that are the same age when looking in either direction. Note that even though a surface of simultaneity for the moving observer includes future images of themselves, those images are space-like separated so the moving observer still only recieves information from the past.

Andrew Hamilton's page with animations about different types of black holes and different coordinate systems

Further reading on the Kerr metric: Book chapter by Matt Visser