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The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation

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For the relativistic uniform system with an invariant mass density the exact expressions are determined for the potentials and strengths of the gravitational field, the energy of particles and fields. It is shown that, as in the classical case for bodies with a constant mass density, in the system with a zero vector potential of the gravitational field, the energy of the particles, associated with the scalar field potential, is twice as large in the absolute value as the energy defined by the tensor invariant of the gravitational field. The problem of inaccuracy of the use of the field’s stress-energy tensors for calculating the system’s mass and energy is considered. The found expressions for the gravitational field strengths inside and outside the system allow us to explain the occurrence of the large-scale structure of the observable Universe, and also to relate the energy density of gravitons in the vacuum field with the limiting mass density inside the proton. Both the Universe and the proton turn out to be relativistic uniform systems with the maximum possible parameters. The described approach allows us to calculate the maximum possible Lorentz factor of the matter particles at the center of the neutron star and at the center of the proton, and also to estimate the radius of action of the strong and ordinary gravitation in cosmological space.


International Letters of Chemistry, Physics and Astronomy (Volume 78)
S. G. Fedosin "The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation", International Letters of Chemistry, Physics and Astronomy, Vol. 78, pp. 39-50, 2018
Online since:
April 2018

[1] S.G. Fedosin, Relativistic energy and mass in the weak field limit, Jordan Journal of Physics. 8(1) (2015) 1-16.

[2] S.G. Fedosin The integral energy-momentum 4-vector and analysis of 4/3 problem based on the pressure field and acceleration field, American Journal of Modern Physics. 3(4) (2014) 152-167.


[3] V.I. Denisov, A.A. Logunov, The inertial mass defined in the general theory of relativity has no physical meaning, Theoretical and Mathematical Physics. 51(2) (1982) 421-426.


[4] R.I. Khrapko, The Truth about the energy-momentum tensor and pseudotensor, Gravitation and Cosmology. 20(4) (2014) 264-273.


[5] S.G. Fedosin, Estimation of the physical parameters of planets and stars in the gravitational equilibrium model, Canadian Journal of Physics. 94(4) (2016) 370-379.


[6] S.G. Fedosin, The virial theorem and the kinetic energy of particles of a macroscopic system in the general field concept, Continuum Mechanics and Thermodynamics. 29(2) (2016) 361-371.


[7] S.G. Fedosin, Two components of the macroscopic general field, Reports in Advances of Physical Sciences. 1(2) (2017).

[8] S.G. Fedosin, The metric outside a fixed charged body in the covariant theory of gravitation, International Frontier Science Letters. 1 (2014) 41-46.


[9] S. Fedosin, The physical theories and infinite hierarchical nesting of matter, Volume 2, LAP LAMBERT Academic Publishing, 2015. ISBN 978-3-659-71511-2.

[10] S.G. Fedosin, The pioneer anomaly in covariant theory of gravitation, Canadian Journal of Physics. 93(11) (2015) 1335-1342.


[11] A. Einstein, Gibt es eine Gravitationswirkung die der elektrodynamischen Induktionswirkung analog ist? Vierteljahrsschrift für gerichtliche Medizin und öffentliches Sanitätswesen. 44 (1912) 37-40.

[12] S.G. Fedosin, Fizika i filosofiia podobiia: ot preonov do metagalaktik, Perm, Russia, 1999. ISBN 5-8131-0012-1.

[13] M. Sharif, Z. Yousaf, Role of adiabatic index on the evolution of spherical gravitational collapse in Palatini f(R) gravity, Astrophys. Space Sci. 355 (2015) 317-331.


[14] Z. Yousaf, M. Zaeem ul Haq Bhatti, Cavity evolution and instability constraints of relativistic interiors, Eur. Phys. J. C. 76 (2016) 267.


[15] Z. Yousaf, M. Zaeem ul Haq Bhatti, U. Farwa, Stability of compact stars in αR2+β(RγδTγδ) gravity, Mon. Not. R. Astron. Soc. 464(4) (2017) 4509-4519.


[16] M. Zaeem ul Haq Bhatti, Z. Yousaf, S. Hanif, Role of f(T) gravity on the evolution of collapsing stellar model, Phys. Dark Universe. 16 (2017) 34-40.


[17] S.G. Fedosin, The procedure of finding the stress-energy tensor and equations of vector field of any form, Advanced Studies in Theoretical Physics. 8(18) (2014) 771-779.


[18] S.G. Fedosin About the cosmological constant, acceleration field, pressure field and energy, Jordan Journal of Physics. 9(1) (2016) 1-30.

[19] S.G. Fedosin, The principle of least action in covariant theory of gravitation, Hadronic Journal. 35(1) (2012) 35-70.

[20] C. Patrignani et al. (Particle Data Group), The review of particle physics, Chin. Phys. C. 40(10) (2016) 100001.

[21] S.G. Fedosin, Cosmic red shift, microwave background, and new particles, Galilean Electrodynamics. 23(1) (2012) 3-13.

[22] S.G. Fedosin, The radius of the proton in the self-consistent model, Hadronic Journal. 35(4) (2012) 349-363.

[23] S.G. Fedosin, The graviton field as the source of mass and gravitational force in the modernized Le Sage's model, Physical Science International Journal. 8(4) (2015) 1-18.


[24] S.G. Fedosin, The charged component of the vacuum field as the source of electric force in the modernized Le Sage's model, Journal of Fundamental and Applied Sciences. 8(3) (2016) 971-1020.


[25] S.G. Fedosin, The Hamiltonian in covariant theory of gravitation, Advances in Natural Science. 5(4) (2012) 55-75.

[26] V.A. Fock, The theory of space, time and gravitation, Macmillan, (1964).

[27] Z. Yousaf, Spherical relativistic vacuum core models in a Λ-dominated era, Eur. Phys. J. Plus. 132(2) (2017) 71.


[28] Z. Yousaf, Stellar filaments with Minkowskian core in the Einstein-Λ gravity, Eur. Phys. J. Plus. 132(6) (2017) 276.

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