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Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

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Spherically-symmetric non-static solutions of Einstein’s equations

https://doi.org/10.29235/1561-2430-2023-59-4-308-314

Abstract

In this paper, we considered non-static vacuum spherically symmetric solutions of the Einstein equations and harmonicity conditions in the coordinate system with a non-zero space-time component in the metric. For the case of the weak field, a particular solution of the approximate equations was obtained, which corresponds to a nonstatic source whose boundary moves with a constant speed. For the exact Einstein’s equations we obtained a wave-type solution, determined by two implicitly specified functions, depending on the retarded argument and on the radial coordinate, respectively. The connection between these solutions and the Birkhoff theorem is discussed.

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ISSN 1561-2430 (Print)
ISSN 2524-2415 (Online)