December 1997
8
Lecture Notes on General Relativity
Sean M. Carroll
Cosmology
Contemporary cosmological models are based on the idea that the universe is pretty much
the same everywhere a stance sometimes known as the Copernican principle. On the
face of
December 1997
6
Lecture Notes on General Relativity
Sean M. Carroll
Weak Fields and Gravitational Radiation
When we rst derived Einsteins equations, we checked that we were on the right track by
considering the Newtonian limit. This amounted to the requir
December 1997
7
Lecture Notes on General Relativity
Sean M. Carroll
The Schwarzschild Solution and Black Holes
We now move from the domain of the weak-eld limit to solutions of the full nonlinear
Einsteins equations. With the possible exception of Minkows
December 1997
5
Sean M. Carroll
Lecture Notes on General Relativity
More Geometry
With an understanding of how the laws of physics adapt to curved spacetime, it is undeniably
tempting to start in on applications. However, a few extra mathematical techniqu
December 1997
4
Lecture Notes on General Relativity
Sean M. Carroll
Gravitation
Having paid our mathematical dues, we are now prepared to examine the physics of gravitation as described by general relativity. This subject falls naturally into two pieces:
Lecture Notes on General Relativity
arXiv:gr-qc/9712019v1 3 Dec 1997
Sean M. Carroll
Institute for Theoretical Physics
University of California
Santa Barbara, CA 93106
carroll@itp.ucsb.edu
December 1997
Abstract
These notes represent approximately one sem
December 1997
2
Lecture Notes on General Relativity
Sean M. Carroll
Manifolds
After the invention of special relativity, Einstein tried for a number of years to invent a
Lorentz-invariant theory of gravity, without success. His eventual breakthrough was t
December 1997
3
Lecture Notes on General Relativity
Sean M. Carroll
Curvature
In our discussion of manifolds, it became clear that there were various notions we could talk
about as soon as the manifold was dened; we could dene functions, take their deriva