Holographic considerations on non-gaussian statistics and gravothermal catastrophe

TL;DR

This paper explores how non-Gaussian statistics, specifically Tsallis and Kaniadakis formalisms, modify gravitational constants and impact gravothermal collapse, revealing potential deviations and equivalences in entropic gravity frameworks.

Contribution

It derives a modified gravitational constant using non-Gaussian statistics and analyzes its effects on gravothermal catastrophe and entropic gravity equivalences.

Findings

Modified gravitational constants are derived from non-Gaussian statistics.

Negative heat capacities are analyzed in the context of gravothermal catastrophe.

Deviations of the modified gravitational constants are quantified.

Abstract

In this paper we have derived the equipartition law of energy using Tsallis formalism and the Kaniadakis power law statistics in order to obtain a modified gravitational constant. We have applied this result in the gravothermal collapse phenomenon. We have discussed the equivalence between Tsallis and the Kaniadakis statistics in the context of Verlinde entropic formalism. In the same way we have analyzed negative heat capacities in the light of gravothermal catastrophe. The relative deviations of the modified gravitational constants are derived.