Vol. 11, no.3, 2019


Dmitry Yu. Tsipenyuk, Vladimir B. Belayev
Prokhorov General Physics Institute of Russian Academy of Sciences, http:// www.gpi.ru/
Moscow 119991, Russian Federation
OPCID: 0000-0001-8367-0883, e-mail: tsip@kapella.gpi.ru
Vladimir B. Belayev
Center for Relativity and Astrophysics, Efremov Research Institute of Electrophysical Equipment, http://www.niiefa.spb.su/
Saint-Petersburg 196641, Russian Federation
E-mail: wbelayev@yandex.ru

Received 23.07.2019, peer reviewed 20.09.2019, accepted 23.09.2019
Abstract. It is considered (1+4)-dimensional Extended Space Model (ESM) as a generalization of the special theory of relativity at a 5-dimensional space. Rotations in extended space correspond to the motion of a particle in gravity field in the embedded four-dimensional space-time. Within the framework of ESM the photons have a nonzero mass in a gravitational field. We study how a rotation in ESM agrees with photon dynamics in the Schwarzschild field. Equations of the critical curve are obtained by the nonzero energy integral variation in accordance with principles of the calculus of variations in mechanics. This method is compared with the Fermat’s principle and geodesics principle. The force vector acting on the photon in Schwarzschild space-time is found for the weak gravity and corresponds to photon’s gravitational mass equal to the twice mass of a material particle of the same energy. Compliance with the law of conservation of energy as a source of gravity leads to the presence of particles with negative gravitational mass and zero kinematic momentum in the results of the annihilation reaction. Accretion of matter onto compact stars results in their absorption of positive energy from the vacuum and the release negative energy in a free deep space. The particles with negative gravitational mass create there antigravitating vacuum with negative pressure. In the present work a non-conservation of energy in gravitational systems is interpreted by the ESM as the rotation of the energy-momentum vector in 5-dimensional space. The comparison bubble cosmic structures of a type gravastar with similar possible bubble structures in microphysical objects is made.

Keywords: photon dynamics, 5-dimensional space, gravity, mass, Fermat’s principle, Schwarzschild space-time, e-p annihilation, gravastar

PACS 04.20.Fy, 04.20.Jb, 11.10.Kk, 13.66.Hk, 97.10.Gz, 98.62.Dm

RENSIT, 2019, 11(2):249-260 DOI: 10.17725/rensit.2019.11.249

Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/297/11(3)249-260e.pdf