Logarithmic correction of the BTZ black hole and adaptive model of Graphene

TL;DR

This paper investigates logarithmic entropy corrections in black holes, using an adaptive graphene model to analyze thermodynamic properties and potentially determine the correct quantum gravity approach.

Contribution

It introduces an adaptive graphene model to study logarithmic corrections in black hole thermodynamics, linking experimental analogs to quantum gravity theories.

Findings

Logarithmic correction coefficients can be experimentally tested using analogous black holes.

Graphene-based models can simulate thermodynamic properties of BTZ black holes.

Results may help identify the correct quantum gravity approach.

Abstract

It is known that almost all approaches to quantum gravity produce a logarithmic correction term to the entropy of a black hole, but the exact coefficient of such a term varies between the different approach to quantum gravity. Such logarithmic terms can also occur due to thermal fluctuations in both analogous and real black holes so that we will analyze the effects of logarithmic corrections term with variable coefficient on properties of analogous black hole. As these properties can be experimentally tested, they can be used to obtain the correct coefficient for such terms for an analogous black hole. We will argue that as even the real black holes can be considered as thermodynamical objects in Jacobson formalism, so such analogous black holes can be used to obtain the correct coefficient for the real black holes, and this in turn can be used to select the correct approach to quantum gravity. In that case, we use an adaptive model of graphene, which is still far from real graphene, to investigate some thermodynamics quantities of BTZ black hole.