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Chapter 2 - The Einstein equation

Published online by Cambridge University Press:  03 April 2025

Justin Corvino  and
Pengzi Miao
Justin Corvino
Affiliation:
Lafayette College, Pennsylvania
Pengzi Miao
Affiliation:
University of Miami
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Summary

The theory of special relativity incorporates a modification of Newtonian mechanics together with electromagnetism. A natural question to consider is how gravitation fits into the framework of relativity. In this chapter we focus our analysis of this question along two main ideas, that of the equivalence between uniform acceleration and a uniform gravitational field, and that of the gravitational redshift. These will lead us to the Einstein equation, which we then show can be given a variational formulation. We present some solutions of the Einstein equation, with particular attention given to the Schwarzschild spacetime and its Kruskal extension.

Keywords

Einstein equationequivalence principlegeneral relativityEinstein-Hilbert actionSchwarzschild spacetime
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Lectures on Mathematical Relativity , pp. 47 - 106
Publisher: Cambridge University Press
Print publication year: 2025

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  • The Einstein equation
  • Justin Corvino, Lafayette College, Pennsylvania, Pengzi Miao, University of Miami
  • Book: Lectures on Mathematical Relativity
  • Online publication: 03 April 2025
  • Chapter DOI: https://doi.org/10.1017/9781139942300.003
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  • The Einstein equation
  • Justin Corvino, Lafayette College, Pennsylvania, Pengzi Miao, University of Miami
  • Book: Lectures on Mathematical Relativity
  • Online publication: 03 April 2025
  • Chapter DOI: https://doi.org/10.1017/9781139942300.003
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • The Einstein equation
  • Justin Corvino, Lafayette College, Pennsylvania, Pengzi Miao, University of Miami
  • Book: Lectures on Mathematical Relativity
  • Online publication: 03 April 2025
  • Chapter DOI: https://doi.org/10.1017/9781139942300.003
Available formats
×