Spherically symmetric wave solution of Einstein's equations in the weak field approximation
https://doi.org/10.29235/1561-8323-2020-64-4-399-402
Abstract
In the linear approximation of general relativity, an exact spherically symmetric non-static solution of Einstein's equations is obtained. It describes a gravitational wave depending on a retarded argument. The non-zero expressions for the momentum density of the wave and the forces acting on a test particle are obtained.
About the Authors
Yu. P. VyblyiBelarus
Vyblyi Yury P. - Ph. D. (Physics and Mathematics), Leading researcher. B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus.
68-2, Nezavisimosti Ave., 220072, Minsk.
A. A. Leonovich
Belarus
Leonovich Anatoly A. - Ph. D. (Physics and Mathematics), Associate professor. Belarusian State University of Informatics and Radioelectronics.
P. Brovka Str., 6, 220068, Minsk.
References
1. Einstein А. Collection of scientific papers, Vol. 1. Moscow, 1965. 514 p. (in Russian).
2. Weinberg S. Gravitation and Cosmolog. Principles and Applications of the General Theory of Relativity. Wiley, 1972. 685 p.
3. Ohanian H., Ruffini R. Gravitation and Spacetime. Cambridge, 2013. 528 p. https://doi.org/10.1017/cbo9781139003391
4. Zakharov V. D. Gravitational Waves in Einstein Theory of Gravity. Moscow, 1972. 199 p. (in Russian).
5. Bichak I., Rudenko V. N. Gravitational Waves in General Relativity and Its Detection Problem. Moscow, 1987. 268 p. (in Russian).
6. Leonovich А. А., Vyblyi Yu. P. Exact solution for spherical gravitational wave in relativistic theory of gravitation. Nonlinear Dynamics and Applications, 2010, vol. 17, pp. 106-110.
7. Karbanovski V. V., Sorokin O. M., Nesterova M. I., Bolotnyaya V. A., Markov V. N., Kairov T. V., Lyash A. A., Tarasyuk O. R. The general class of the vacuum spherically symmetric equations of the general relativity theory. Journal of Experimental and Theoretical Physics, 2012, vol. 115, no. 2, pp. 208-211. https://doi.org/10.1134/s1063776112070084
8. Vyblyi Yu. P., Leonovich А. А. Spherically-Symmetric Nonstatic Gravitational Fields in tensor Theory of Gravity. Sbornik trudov LIV Vserossiiskoi konferentsii po problemam dinamiki, fiziki chastits, fiziki plazmy i optoelektroniki [Proceedings LIV Russian Conference on Problems of Dynamics, Particle Physics, Plasma Physics and Optoelectronics]. Moscow, 2018, pp. 31-34 (in Russian).
9. Leonovich A. A., Vyblyi Yu. P The Classical Energy-Momentum Problem and Fock Tensor. Nonlinear Phenomena in Complex Systems, 2018, vol. 2, no. 4, pp. 406-410.