Lecture Notes on General Relativity [gr-qc/9712019]

[ajb]

Lecture Notes on General Relativity

Sean M. Carroll

 

These online notes are the best introduction to general relativity "proper" I have seen. Carroll does not shy away from the basics of differential geometry needed to understand relativity theory.

 

Carroll starts with a good review of special relativity paying attention to the more geometric (tensorial) issues. This sets one up to proceed to general relativity with "minimal pain". To do this the elementary theory of manifolds and curvature is discussed. Mostly, this is done using local theory via coordinates.

 

It is not till chapter 4 that gravity is discussed. The apparent delay is unavoidable if one wants to discuss more than a trivial overview of general relativity.

 

The notes then proceed to discuss more advanced issues in geometry, mostly pull-backs, diffeomorphisms and Lie derivatives. All needed in any real discussion of relativity.

 

On the physics side weak fields, black holes and cosmology are discussed. The notes are now a little old to include some of the latest results in cosmology, but I would not let that put you off in any way.

 

Outline

0) Introduction

1) Special Relativity and Flat Spacetime

2) Manifolds

3) Curvature

4) Gravitation

5) More Geometry

6) Weak Fields and Gravitational Radiation

7) The Schwarzschild Solution and Black Holes

8) Cosmology

 

 

I fully recommend these notes.

 

These notes have been updated and formulated into a book "Spacetime and Geometry: An Introduction to General Relativity" Addison Wesley; illustrated edition edition (16 Oct 2003).

 

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@Article{Carroll:1997ar,

author = "Carroll, Sean M.",

title = "{Lecture notes on general relativity}",

year = "1997",

eprint = "gr-qc/9712019",

archivePrefix = "arXiv",

SLACcitation = "%%CITATION = GR-QC/9712019;%%"

}