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1 results

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

  • from Part II - The theory of gravitation
  • Jerzy Plebanski, National Polytechnic Institute of Mexico, Andrzej Krasinski, Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences
  • Book:
    An Introduction to General Relativity and Cosmology
    Published online:
    30 May 2024
    Print publication:
    06 June 2024, pp 123-155

  • 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.