The General Relativity Tutorial
This is bunch of interconnected web pages that serve as an informal
introduction to that beautiful and
amazingly accurate theory of gravity called
general relativity. The goal is to
explain the basic equation in this theory - Einstein's equation -
with a minimum of fuss and muss.
You can begin by reading this:
Clicking on any of the underlined key concepts will then take you
to the corresponding point in this more detailed:
In the long course outline, clicking on any underlined key concept will
take you to a still more detailed exposition of that concept.
A more formal presentation of this material can be found here:
including some extra stuff, but leaving out many other things.
Alternatively, you can dive right in and read the adventures
This is the fun part! In these stories, the hapless peasant
Oz learns general relativity from a grumpy but powerful wizard.
But, unless you are already familiar with general relativity, to
understand these adventures you will need to look at the other material
from time to time.
All this material originated on the newsgroup
Much of it is written by Oz and I, but there are also substantial
contributions by Ted Bunn, Ed Green, Keith Ramsay, Bruce Scott, Bronis
Vidugiris, and Michael Weiss.
You can also get
as it actually occurred on sci.physics.
This has much more detail than the material above, and it's
a lot of fun, but it's a bit disorganized. If someone wants to
make webpages out of this stuff, please do - and let me have
General relativity is usually written with lots of
superscripts and subscripts. Mitchell Charity has kindly
improved these web pages so that they look nice.
However, not all old web browsers can handle this.
If you don't see the
word `superscript' raised
in this sentence, click here,
and you will get the old version of these pages, without nice-looking
superscripts and subscripts.
This tutorial is no substitute for reading books on general
relativity and doing the exercises - just
like dipping your toe in the ocean is no substitute for
learning to swim.
You should start by checking out Chris Hillman's stuff
on the World-Wide Web. There are some nice books available
for free online!
Unfortunately, the best books on general relativity still cost money.
But, they're worth the price. So:
Here are four nontechnical introductions, all
quite different in flavor. You can't really learn the details
of general relativity from these books, but they're written
by world-class experts, and they're a great way to get an intuitive
feel for the subject:
Kip S. Thorne, Black Holes and Time Warps: Einstein's Outrageous
Legacy, W. W. Norton, New York, 1994.
Robert Geroch, General Relativity from A to B,
University of Chicago Press, Chicago, 1978.
Bernard F. Schutz, Gravity from the Ground Up: An Introductory
Guide to Gravity and General Relativity, Cambridge University
Press, Cambridge, 2003.
Robert M. Wald, Space, Time, and Gravity: the Theory of the Big Bang
and Black Holes, University of Chicago Press, Chicago, 1977.
Before you get serious about learning general relativity, it helps to
have special relativity down cold. For this, try:
Edwin F. Taylor, John A. Wheeler, Spacetime Physics: Introduction to
Special Relativity, W. H. Freeman Press, New York, 1992.
When you're ready to actually dive into general relativity,
you might start with one of these books:
Ray d'Inverno, Introducing Einstein's Relativity, Oxford
University Press, Oxford, 1992.
James B. Hartle, Gravity: an Introduction to Einstein's
General Relativity, Addison-Wesley, New York, 2002.
Ian R. Kenyon, General Relativity,
Oxford University Press, Oxford, 1991.
Bernard F. Schutz, A First Course in General Relativity, Cambridge
University Press, Cambridge, 1986.
Hans Stephani, General Relativity: An Introduction to the Theory of
the Gravitational Field, Cambridge U. Press, Cambridge, 1990.
And when you want to really master general relativity, you'll have
to read the classics:
Charles W. Misner, Kip S. Thorne and John Archibald Wheeler,
Gravitation, W. H. Freeman Press, San Francisco, 1973.
Robert M. Wald, General Relativity, University of Chicago Press,
If you want to bone up on your geometry before getting
deeper into general relativity you should check out:
Barrett O'Neill, Semi-Riemannian Geometry: with Applications to
Relativity, Academic Press, New York, 1983.
To be honest, I must admit to having written a book dealing with
general relativity myself:
John Baez and Javier P. de Muniain, Gauge Fields, Knots, and Gravity,
World Scientific Press, Singapore, 1994.
It concentrates on the mathematics of general relativity and other gauge
fields, such as Maxwell's equations and the Yang-Mills equations, which
describe the strong and electroweak forces.
"Newton, forgive me; you found the only
way which, in your age, was just about possible for a man of highest
thought and creative power" - Albert Einstein
© 2006 John Baez