How to Cite

Bartelmann, Matthias: General Relativity, Heidelberg: Heidelberg University Publishing, 2019 (Lecture Notes). https://doi.org/10.17885/heiup.534

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Identifiers

https://doi.org/10.17885/heiup.534
ISBN 978-3-947732-59-3 (PDF)
ISBN 978-3-947732-60-9 (Softcover)

Published

10/10/2019

Downloads

Download book (PDF/6MB)
Statistic

Authors

Matthias Bartelmann

General Relativity

Lecture Notes

Einstein‘s theory of general relativity is still the valid theory of gravity and has been confirmed by numerous tests and measurements. It is built upon simple principles and relates the geometry of space-time to its matter-energy content. These lecture notes begin by introducing the physical principles and by preparing the necessary mathematical tools taken from differential geometry. Beginning with Einstein’s field equations, which are introduced in two different ways in the lecture, the motion of test particles in a gravitational field is then discussed, and it is shown how the properties of weak gravitational fields follow from the field equations. Solutions for compact objects and black holes are derived and discussed as well as cosmological models. Two applications of general relativity to astrophysics conclude the lecture notes.

Matthias Bartelmann is professor for theoretical astrophysics at Heidelberg University. He mostly addresses cosmological questions, concerning in particular the formation and evolution of cosmic structures.

Chapters

Table of Contents
Pages
PDF
Title
Instead of a preface
v
Contents
vii–x
1 Introduction
1–13
2 Differential Geometry I
15–29
3 Differential Geometry II
31–46
4 Physics in Gravitational Fields
47–61
5 Differential Geometry III
63–76
6 Einstein’s Field Equations
77–90
7 Weak Gravitational Fields
91–109
8 The Schwarzschild Solution
111–125
9 The Schwarzschild Spacetime
127–141
10 Schwarzschild Black Holes
143–159
11 Charged, Rotating Black Holes
161–181
12 Homogeneous, Isotropic Cosmology
183–198
13 Relativistic Astrophysics
199–212
Appendix A Electrodynamics
213–215
Appendix B Differential Geometry
217–225
Appendix C Penrose-Carter diagrams
227–229
Index
231–234

Comments