Holographic considerations on non-gaussian statistics and gravothermal catastrophe

The mechanism of gravothermal instability, discovered by Antonov is an important phenomena in gravitational thermodynamics. It has been very helpful for an extensive research concerning statistical mechanics of long range interactions systems in several fields in physics. This connection with thermodynamics and statistical mechanics has motivated us to investigate statistically the gravothermal catastrophe

At the same time, there are theoretical evidences that the understanding of gravity has been greatly benefited from a possible connection with thermodynamics. Pioneering works of Bekenstein and Hawking have described this issue. For example, quantities as area and mass of black-holes are associated with entropy and temperature respectively. Working on this subject, Jacobson interpreted Einstein field equations as a thermodynamic identity. Padmanabhan gave an interpretation of gravity as an equipartition theorem.

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's entropic formalism.
In the same way we have analyzed the negative heat capacities in the light of gravothermal catastrophe.
The relative deviations of the modified gravitational constants are derived.