General Relativity is the theory of gravitation introduced by Einstein in 1915, and developed throughout the 20th century. And you’ve decided you want to learn it. But why spend hundreds of dollars on textbooks? It’s easy to learn things on the cheap, without sacrificing quality. And in this tutorial, I’ve compiled a list of introductory material on the physics and philosophy of general relativity, all of which is available for free online. If you know of any online resources that are not on this list, suggest them in the comments and I will add them to the list!
- Non-mathematical introductions to general relativity
- Mathematical introductions to general relativity
- Philosophy of general relativity
- Other general relativity references.
Non-mathematical introductions to general relativity
- Einstein for Everyone, by John D. Norton. This is a complete introductory text. Many pictures and animations illustrating the central features of the theory. Emphasizes philosophical perspectives, where relevant. Available for free online.
- Introduction to General Relativity on Wikipedia. A quick overview of a few of the essential features of GR, on everyone’s favorite non-scholarly resource.
Mathematical introductions to general relativity
- Oz and the Wizard, by John Baez. This is very entertaining introduction to general relativity in the form of a dialogue. It also contains a fantastic dictionary of common terms in GR.
- David Malament’s lecture notes on GR (PDF) are an incredible resource, and the standard relativity textbook for philosophers of physics, in that Malament emphasizes mathematical and philosophical perspectives. It has no been published as a book.
- Lecture notes on general relativity, by Sean M. Carroll. These are the course lectures for an MIT graduate course in general relativity, and have also been turned into a book. Also try the 24-page “no-nonsense” version of these notes (PDF).
- Introduction to Differential Geometry and General Relativity, by Stefan Waner. A beautifully arranged collection of lecture notes on differential geometry. Approach is highly mathematical, taking the reader from basic point-set topology all the way to Einstein’s field equations.
- Tensors and Relativity, by Peter Dunsby. A first course in general relativity, beginning with special relativity. Includes an “assignments” section with hints. The layout is ugly and cumbersome, but the content is good.
- Introduction to General Relativity (PDF), by Gerald ‘t Hooft. These lecture notes have since been turned into a book with Wei Chen.
- Modern Relativity, by David Waite. A first course on general relativity, which assumes good familiarity with special relativity. Includes exercises.
Philosophy of general relativity
- Here are some undergraduate and graduate courses that deal with the Philosophy of Relativity (with tons of resources), taught by some of the leaders in the field:
- John Earman and John Norton, Pitt HPS 2534: General Relativity and Gravitation
- David Malament, UC Irvine LPS 141: Geometry and Spacetime (special relativity)
- Jonathan Bain, NYU PL 2283: Philosophy of Relativity
- Craig Callendar, UCSD Phil 146: Philosophy of Physics
- Christian Wüthrich, UCSD Phil-146: Philosophy of Space and Time
- John Norton’s Introduction to the Philosophy of Space and Time gives Norton’s characteristically clear (and opinionated) view of the field. Most of Norton’s papers on the philosophy of general relativity are available here.
- David Malament’s Classical General Relativity describes the mathematical structure of the theory, and introduces a few of the philosophical problems associated with it. Most of Malament’s papers on the philosophy of general relativity are available here.
- The Philsci Archive’s Relativity category contains most of the latest preprints in the philosophy of general relativity. (I have written some tips for using this resource.)
- John Earman v. Tim Maudlin: Two philosophy of physics giants discuss what general relativity teaches us about the nature of time. (Not really introductory, but too entertaining not to mention).
Other general relativity resources.
- Black Holes, by Paul Townsend. From his Cambridge course on the black hole physics developed in the 60’s and 70’s.
- The Relativity Bookshelf at U. Toronto is brief but informative.
- Arxiv.org’s general relativity category, on the other hand, is like drinking from a fire-hose. Hundreds of articles on general relativity appear every week.
That’s all the free general relativity for today. Enjoy!
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