**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32020

##### The Relationship between the Energy of Gravitational Field and the Representative Pseudotensor

**Authors:**
R. I. Khrapko

**Abstract:**

As is known, the role of the energy-momentum pseudotensors of the gravitational field is to extend the conservation law to the gravitational interaction by taking into account the energy and momentum of the gravitational field. We calculated the contribution of the Einstein pseudotensor to the total mass of a stationary material body and its gravitational field. It turned out that this contribution is positive, despite the fact that the mass-energy of a stationary gravitational field is negative. We concluded that the pseudotensor incorrectly describes the energy of the gravitational field. Nevertheless, this pseudotensor has been used in a large number of scientific works for 100 years. We explain this by the fact that the covariant component of the pseudotensor was regarded as the mass-energy. Besides, we prove the advantage of the covariant energy-momentum conservation law for matter in the Minkowski space-time.

**Keywords:**
Conservation law,
covariant integration,
gravitation field,
isolated system.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1474347

**References:**

[1] A. Guth, The Inflationary Universe: The Quest for a New Theory of Cosmic Origins, Random House, 1997.

[2] A. Einstein, “Das hamiltonisch.es Prinzip und allgemeine Relativitatstheorie,” Sitzungsber. preuss. Akad. Wiss., 1916, 2, pp. 1111—1116.

[3] R. C. Tolman, Relativity Thermodynamics and Cosmology, Dover Books on Physics, 2011.

[4] A. S. Eddington, The mathematical theory of relativity, Cambridge University Press, 2010.

[5] L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, Pergamon, N. Y., 1975.

[6] K. Schwarzschild, Berl. Ber. 1916, p. 424. For an English translation see “On the Gravitational Field of a Sphere of Incompressible Fluid according to Einstein’s Theory,” arXiv:physics/9912033.

[7] R. C. Tolman, “On the Use of the Energy-Momentum Principle in General Relativity,” Phys. Rev. 35, p. 875, 1930.

[8] R. I. Khrapko, “Goodbye, the Pseudotensor,” Abstracts of ICGAC-12, Moscow, 2015. http://khrapkori.wmsite.ru/ftpgetfile.php?id=141&module=files

[9] R. I. Khrapko “Path-dependent functions” Theoretical and Mathematical Physics. Volume 65, Issue 3, (1985), p. 1196

[10] R. I. Khrapko, “Example of creation of matter in a gravitation field”, Sov. Phys. JETP 35 (3), 441 (1972)

[11] A. Einstein, “Über Gravitationswellen”.Sitzungsberichte. preuss. Akad. Wiss., 1918, 1, 154—167.