A remarkable connection between the Jeans’ theory of gravitational instabilities and the Newtonian limit of the General Theory of Relativity

0574267 - MÚ 2024 RIV BG eng J - Journal Article
Křížek, Michal - Mészáros, A.
A remarkable connection between the Jeans’ theory of gravitational instabilities and the Newtonian limit of the General Theory of Relativity.
Bulgarian astronomical journal. Roč. 39, July (2023), s. 28-35. ISSN 1313-2709
Institutional support: RVO:67985840
Keywords : gravitational potential * Jean's theory * Newtonian limit * Poisson equation
OECD category: Astronomy (including astrophysics,space science)
Impact factor: 0.4, year: 2022
Method of publishing: Open access
https://astro.bas.bg/AIJ/issues/n39/MKrizek.pdf

We investigate both the Newtonian limit of the General Theory of Relativity and the Jeans’ theory of gravitational instabilities in order to obtain some new conclusions on these two classical topics. We use the standard method for calculating the Ricci tensor by means of the Christoffel symbols of the second kind in the Newtonian limit. We assume that both the gravitational potential and the mean mass density can depend on time. The density of the non-relativistic dust can also be time dependent. As an impact on the Jeans’ theory, we confirm that the modifications done by Lifshitz in 1946 and by Bonnor in 1957 are perfect and hold. In the Poisson equation the time dependence of both sides is an original new development. The application of this on the Jeans’ theory is then straightforward.
Permanent Link: https://hdl.handle.net/11104/0344608