In 1996 I taught a one-semester graduate course graduate course in
general relativity at MIT. Along the way I typed up a detailed set
of lecture notes; in a slightly polished form, these are available
online as Lecture Notes on General Relativity.
The book Spacetime and Geometry is a significantly
revised and expanded version of these notes; about half of the
finished book is completely new. The lecture notes will continue to be
available for free online.
The philosophy of the book is to provide an accessible, useful, and
pedagogical introduction to general relativity. In particular, no
effort has been made to write a comprehensive reference book.
More on the approach taken can be found in the
You can order the book online from
Amazon.com or from
Why spend money on the book if the lecture notes are free?
You don't have to spring for the book, of course; the lecture notes
remain pretty good. But there are still reasons to reach
for your wallet. First there are practical issues --- it's much nicer
to have a book in your hands than a printout; the cover (right) is
aesthetically pleasing; the organization is a little more clear
(subsections, figure captions); and perhaps best of all there
is an index. Next there is the additional material appearing only
in the book version --- notably a section on QFT in curved spacetimes
and a vastly expanded discussion of cosmology, but also smaller
bits on classical field theory, conformal transformations, maximally
symmetric spaces, alternative theories, the cosmological constant,
experimental tests, degrees of freedom, Stokes's theorem, gravitational waves,
gravitational lensing, hypersurfaces and congruences,
properties of event horizons, and more. All in all, only about 50%
of the book is taken from the lecture notes. (See the
Finally, the entire manuscript has received a thorough going-over
to polish and improve the presentation as much as possible.
An effort has been made to include more physically relevant examples
right from the start, so that new pieces of mathematics are immediately
put to work in a useful context; I have also moved a great deal of
mathematics to a set of appendices, to provide more flexibility
to instructors. Some
of the changes are subtle, but they add up to a significant
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