General Relativity

Spring 2026

News:

I will have office hours on Tuesday. Other than a department meeting at noon, I should be in all day.

The final problem set is posted!

Course Info and Documents (pdf):

Course Info:

Course Syllabus (v1.5)

Problem Sets (pdf):

Links:

• SR: A translation of "Electrodynamics of Moving Bodies", Einstein's original 1905 paper on special relativity. Here's a pdf of the original article in German pubished in Annalen der Physik.
• SR: The first principle of relativity is Galileo's. Here's the quote from Galileo on the ship's cabin in the Dialog.
• SR: Beautiful animations of the apparent geometry of relativistically moving objects. The dice and the ride down Marktgasse in Tuebingen are particularly good. Note, however, that red/blueshift is not accounted for.
• MATH: A handy listing of hyperbolic trig function identities.
• GR: A piece by Dennis Overbye on the second image of M87 by the Event Horizon Telescope. The newly released image is on the top right of the page.
• GR: A short popular science piece on the equivalence principle.
• GR: A demonstration of the parallel transport on a sphere (uses Mathematica).
• GR: A link to the paper (pdf) by Baez and Bunn on the meaning of the Einstein equations. For an older published version see Amer. Jour. Phys. 73 (2005) 644-652.
• GR: There are recent results on exploring spacetime with light and black holes. See the piece by Denis Overbye in the NYTimes. The movie of null geodesics is absolutely amazing! The original article (pdf).
• GR: About the stunning visualizations of black holes in Interstellar.
• GR: Wee, light cones! Lillie found this link to some visualizations, including of the warp drive light cone structure.
• GR: Tensor computation! Here's the pdf of the mathematica introduction. There are now additional choices for tensor computation. These include xAct and OGRe (This last link is to the paper introducing the package. See also OGRePy for a object oriented tensor calculations in python.)
• GR: There is the python package EinsteinPy for tensor calculations in python.
• GR: Here's the html version of the "einstein.nb" (nb) Mathematica notebook.
• GR: k=0 Roberston-Walker in native (nb) mathematica, html, and text forms.
• GR: The comological model notebook (nb) used in class.
• GR: A piece by Cliff Will on the Gravity Probe B experiment.
• GR: A 30 year review (pdf) on the Hulse-Taylor binary pulsar.
• GR: Talk slides (pdf) on binary pulsars.
• GR: We talked about cosmological models that are isotropic. But they may not be. Here are some new results that might suggest anistropy in expansion rates. (Anisotropic models exists in GR too!)
• GR: A simulation of the effects an observer with angular momentum falling into a black hole would see. This page has a rich array of information about the environment around a black hole is like.
• GR: A MIT News piece on Ray Weiss's initial work on what became LIGO.
• GR: The GW discovery paper on GW 150914 from LIGO and a simulation of the event. A video of the event GW190412.

Additional Reading:

• Jim Hartle, Gravity: An Introduction to Einsetin's General Relativity
• Dan Styer, Relativity for the Questioning Mind
• Elis and Williams, Flat and Curved Spacetimes 
• Kip Thorne, The Science of Interstellar
• Kip Thorne, Black Holes, Warp Drives, and Einstein's Outrageous Leagacy
• Dennis Overbye, Einstein in Love (A wonderful ``1st half" biography of Einstein. It ends in 1919.)
• Abraham Pais, Subtile is the Lord (A full biography of Einstein with a careful treatment of the science.)
• (For fun) Paul Krugman's The Theory of Interstellar Trade written many years ago.(My goodness! It was published in 2010.)

Last modified 11 May 2026