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12 - The Einstein equations and the sources of a gravitational field

from Part II - The theory of gravitation

Published online by Cambridge University Press:  30 May 2024

Jerzy Plebanski
Affiliation:
National Polytechnic Institute of Mexico
Andrzej Krasinski
Affiliation:
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences
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Summary

The derivation of the Einstein equations is presented following Einstein’s method. Hilbert’s derivation (from a variational principle) is also presented. The Newtonian limit of Einstein’s theory is discussed. A Bianchi type I solution of Einstein’s equations with a dust source is derived. A brief review of other theories of gravitation (Brans–Dicke, Bergmann–Wagoner, Einstein–Cartan and Rosen) is presented. The matching conditions for different metrics are derived. The weak-field approximation to general relativity is presented.

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Publisher: Cambridge University Press
Print publication year: 2024

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