JOCH-220822

The Universal Euler Equation in Einstein Real Gravity
22 August 2022

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Abstract

Making use of the Bianchi identity together with the Yilmaz exponential parametrization of General Relativity with the so-called tensor potentials describing the physical gravitational field, a universal hydrodynamical Euler equation is derived for a general relativistic fluid. This novel relationship remains valid in the presence of gravitational waves, as it takes into account the full tensorial character of the gravitational field. As a special case, we recover the general hydrodynamical evolution formula for the single component newtonian gravitational field of a relativistic fluid. An important application is the re-analysis of perturbative Jeans' theory of gravitational instability and the study of sound waves in the presence of a gravitational field and their interaction with gravitational waves.

Copyright © 2022 Yvan Leblanc. All rights reserved

PACS: 4.60.+n, 11.17.+y, 97.60.Lf

Cite as: Leblanc, Y., "The Universal Euler Equation in Einstein Real Gravity", Journal of Cosmology, Vol. 26, No. 26, pp 15346 - 15358 (2022).