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)
References
1. Birkhoff G. Relativity and Modern Physics. Harvard University Press, 1923. 283 p. https://doi.org/10.1126/science.58.1513.539
2. Poincare H. Sur la dynamique de l’electron. Rendiconti del Circolo matematico di Palermo, 1906, vol. 21, pp. 129–176. https://doi.org/10.1007/bf03013466
3. Birkhoff G. Flat space–time and gravitation. Proceedings of the National Academy of Sciences, 1944, vol. 30, no. 10, pp. 324–334. https://doi.org/10.1073/pnas.30.10.324
4. Gupta S. Quantization of Einstein’s Gravitational Field: General Treatment. Proceedings of the Physical Society. Section A, 1952, vol. 65, no. 8, pp. 608–619. https://doi.org/10.1088/0370-1298/65/8/304
5. Thirring W. E. An alternative approach to the theory of gravitation. Annals of Physics, 1961, vol. 16, no. 1, pp. 97–117. https://doi.org/10.1016/0003-4916(61)90182-8
6. Deser S. Self–interaction and gauge invariance. General Relativity and Gravitation, 1970, vol. 1, pp. 9–18. https://doi.org/10.1007/bf00759198
7. Feynman R. Feynman Lectures on Gravitation. CRC Press, 2018. 296 p. https://doi.org/10.1201/9780429502859
8. Logunov A., Mestvirishvili M. A. Relativistic theory of gravitation. Progress of Theoretical Physics, 1985, vol. 74, no. 1, pp. 31–50. https://doi.org/10.1143/ptp.74.31
9. Fronsdal C. On the theory of higher spin fields. Il Nuovo Cimento, 1958, vol. 9, pp. 416–443. https://doi.org/10.1007/bf02747684
10. Barnes K. J. Lagrangian theory for the second-rank tensor field. Journal of Mathematical Physics, 1965, vol. 6, pp. 788–794. https://doi.org/10.1063/1.1704335
11. Fock V. The Theory of Space, Time and Gravitation. Pergamon Press – Macmillan Company, 1964. 411 p. https://doi.org/10.1016/b978-0-08-010061-6.50012-3
12. Landau L., Lifshitz E. M. The Classical Theory of Fields. Oxford, Pergamon Press, 1975. 402 p.
13. Leonovich A., Vyblyi Yu. Fock energy-momentum tensor in Relativistic Theory of Gravitation. Methods of NonEuclidian Geometry in Modern Physics: Proceedings of the V International Conference. Minsk, 2007, pp. 207–211.
14. Leonovich A., Vyblyi Yu. The classical energy-momentum problem and Fock tensor in relativistic theory of gravitation. Nonlinear Phenomena in Complex Systems, 2018, vol. 21, no. 4, pp. 406–410.
15. Chernikov N., Tagirov E. A. The theory of conformal-invariant scalar field. Annales de l’Institut Henri Poincaré, 1968, vol. A9, pp. 109–141.
16. Oppenheimer J. R., Snyder H. On unlimited gravitational pressing. Physical Review, 1939, vol. 56, pp. 455–462. https://doi.org/10.1103/physrev.56.455
17. Weinberg S. Gravitation and Cosmology. New York, Wiley, 1972. 657 p.
18. Ohanian, Н. С., Ruffini R. Gravitation and Spacetime. Cambridge University Press, 2013. 528 p. https://doi.org/10.1017/cbo9781139003391
19. Poisson E., Will C. Gravity. Cambridge University Press, 2014. 780 p. https://doi.org/10.1017/cbo9781139507486
Review
Views:
261
Email this article 