We consider variation of energy of the light-like particle in the pseudo-Riemann space-time, find lagrangian, canonical momenta and forces. 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 for the stationary gravity field. The produced equations are solved for the metrics of Schwarzschild, FLRW model for the flat space and Gödel. For these spaces effective mass of light-like particle is established. Relativistic analogue of inertial mass for photon is determined in central gravity field in empty space.
The pressure of the vacuum is detected as per the geometry of the space around the local gravity system according to Sakharov's idea of a "metrical elasticity" of space, i.e., of the emergence of a generalized force, preventing distortion of space. It is assumed that energy equivalent to the gravitational defect of masses is spent on vacuum deformation. We determine the gravitational impact of matter on the vacuum in case of weakly gravitating static centrally symmetric distribution of matter. Opposite in the sign pressure of vacuum corresponds to appropriate solution of Einstein's equations. It can be used to determine the course of time below the Earth's surface.
Динамика частиц в гравитационном поле исследуется с использованием механики Лагранжа. Получен ы динамические уравнения, включающие скорость передачи энергии и импульса гравитационному полю. Рассмотрено движение частиц в поле Шварцшильда и в случае слабой гравитации определены пассивные гравитационные массы фотона и материальной частицы при условии слабого влияния гравитационного поля на ее движение. Найдена активная гравитационная масса для частного случая системы из двух одинаковых тел, движущихся в противоположных направлениях.
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. Energy and momentum of the particle transferred to the gravity field is defined. 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. Bubble gravitational structures of a type gravastar are considered. 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 with similar possible bubble structures in microphysical objects is made.
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