Thermodynamic Interpretation of the Field Equations of BTZ Charged Black Hole near the Horizon

TL;DR

This paper demonstrates that the field equations of a charged BTZ black hole near the horizon can be interpreted as a thermodynamic identity, revealing intrinsic thermodynamic properties of the black hole.

Contribution

It shows how the field equations of a charged BTZ black hole near the horizon can be expressed as a thermodynamic relation, extending previous work to include electric charge.

Findings

Field equations near the horizon can be written as dE=TdS+PdA+PhidQ

Black hole field equations possess intrinsic thermodynamic properties

Thermodynamic interpretation applies to charged BTZ black holes

Abstract

As is already known, a spacetime horizon acts like a boundary of a thermal system an we can associate with it notions as temperature and entropy. Following the work of M. Akbar, in this paper we will show how it is possible to interpret the field equation of a charged BTZ black hole near horizon as a thermodynamic identity dE=TdS+PdA+PhidQ, where Phi is the electric potential and Q is the electric charge of BTZ black hole. These results indicate that the field equations for the charged BTZ black hole possess intrinsic thermodynamic properties near horizon.