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1 results

  • 20 - Relativistic cosmology V: the Szekeres geometries

  • 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 391-441

  • Summary

    The family of the Szekeres–Szafron, shell solutions of Einstein’s equations, is derived and discussed in detail. The discussion contains, among other things, the interpretation of the Szekeres coordinates, the invariant definitions of the whole family, the class II ($\beta,_z = 0$) family as a limit of the class I family, matching the Szekeres metric to the Schwarzschild metric (the class II S metric can be matched to Schwarzschild only inside the event horizon), conditions for absence of shell crossings, the description of the mass dipole, the apparent horizons, the Goode–Wainwright representation and a brief listing of recommended further reading on geometric and astrophysical properties of these solutions.