Relativity and Cosmology

   

Energy Conservation in General Relativity

Authors: Stefan Bernhard Ruester, Antonino Del Popolo

This article shows that the vanishing covariant divergence of the energy-momentum tensor of the matter is a conservation law. Furthermore, it is explained why energy-momentum pseudotensors of the gravitational field cannot represent its energy density, but this is described up to a factor by the Einstein tensor. The necessarily existing conservation law of total energy, momentum, and stress in general relativity is derived, thereby explaining the phenomena of dark energy and dark matter and solving the cosmological constant problem and the cuspy halo problem. In Newton's theory of gravity, it is the modified Poisson equation that fulfills the requirement of conservation of total energy. Using a model that solves the modified Poisson equation, it turns out that dark matter in modified Newtonian cosmology is nothing other than a central point-like mass, probably a supermassive primordial black hole, thus refuting the cosmological principle and explaining both the Hubble and S_8 tensions. A simple but fairly accurate model is presented that solves the modified Poisson equation to fit the calculated rotation curves to the observed speeds in spiral galaxies, which consist of several components: the central black hole, the bulge, the disk, and the dark matter.

Comments: 10 Pages. 1 figure, 1 table, Parana J. Sci. Educ., v.11, n.6, (1-10), December 1, 2025

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[v1] 2025-11-07 23:47:00

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