How to Cite

Schäfer, Björn Malte: General Relativity: Geometric Structure and Dynamics of Spacetime, Heidelberg: Heidelberg University Publishing, 2022 (Lecture Notes). https://doi.org/10.17885/heiup.1056

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Creative Commons License

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

Identifiers

https://doi.org/10.17885/heiup.1056
ISBN 978-3-96822-126-7 (PDF)
ISBN 978-3-96822-164-9 (Softcover)

Published

12/15/2022

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Authors

Björn Malte Schäfer

General Relativity

Geometric Structure and Dynamics of Spacetime

Lecture Notes

General relativity is the theory of the structure and dynamics of spacetime. These lecture notes provide an introduction into the concepts of differential geometry, in particular pseudo-Riemannian geometry, and discusses the ideas behind the construction of a gravitational field equation. Exact solutions to the field equation for highly symmetric spacetimes, i.e. black holes, FLRW cosmologies and gravitational waves, are worked out. Advanced topics that are covered include Lie derivatives and the Killing equation, the derivation of the field equations from variational principles, and the formulation of field theories on curved spacetimes.

Björn Malte Schäfer works at Heidelberg University on problems in modern cosmology, relativity, statistics, and on theoretical physics in general.

Chapters

Table of Contents
Pages
PDF
Front matter
Contents
V–VI
A Relativity and gravity
1–19
B Topological and metric structure of spacetime
21–37
C Differential structure of spacetime and curvature
39–43
D Sources of the gravitational field
45–52
E Gravitational field equation
53–62
F Black holes
63–82
G Friedmann-universes
83–96
H Weak field gravity and gravitational waves
97–107
I Gravity from a variational principle
109–124
X Mathematical supplement
125
Index
129–130

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