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.
Keywords
theory of gravity,
Einstein’s equations,
Birkhoff theorem,
spherical symmetry,
nonstatic solutions,
gravitational wave
Supporting agencies: The work was carried out with the support of the Belarusian Republican Foundation for Basic Research (grant no. Ф22МЦ-005).
About the Authors
Yu. P. Vyblyi
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus
Belarus
Yuri P. Vyblyi – Ph. D. (Physics and Mathematics), Leading Researher
68-2, Nezavisimosti Ave., 220072, Minsk, Republic of Belarus
A. A. Leonovich
Belarussian State University of Informatics and Radioelectronics
Belarus
Belarus
Anatoli A. Leonovich – Ph. D. (Physics and Mathematics), Associate Professor
6, P. Brovka Str., 220013, Minsk, Republic of Belarus)
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