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Symmetry Transformations in Cosmological and Black Hole Analytical Solutions
Version 1
: Received: 8 March 2024 / Approved: 11 March 2024 / Online: 11 March 2024 (18:10:29 CET)
A peer-reviewed article of this Preprint also exists.
León, E.A.; Sandoval-Rodríguez, A. Symmetry Transformations in Cosmological and Black Hole Analytical Solutions. Symmetry 2024, 16, 394. León, E.A.; Sandoval-Rodríguez, A. Symmetry Transformations in Cosmological and Black Hole Analytical Solutions. Symmetry 2024, 16, 394.
Abstract
We analyze the transformation of a very broad class of metrics that can be put in terms of static coordinates. Starting from a general ansatz, we obtain a relation for the parameters in which one can impose further symmetries, or restrictions. One of the simplest restrictions leads to FLRW cases, while transforming from the initial static to other static-type coordinates can lead to near horizon coordinates, Wheeler-Regge, isotropic coordinates, among others. As less restrictive cases, we show an indirect route for obtaining Kruskal-Szekeres within this approach, as well as Lema\^{\i}tre coordinates. We use Schwarzschild spacetime as prototype for testing the procedure in individual cases. However, application to other spacetimes, such as de-Sitter, Reissner-Nordstr\"{o}m or Schwarzschild de Sitter, can be readily generalized.
Keywords
Analytical solutions; Black holes; Cosmology
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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