Thermodynamics of the Three-dimensional Black Hole with a Coulomb-like Field

TL;DR

This paper investigates the thermodynamics of a (2+1)-dimensional black hole with a Coulomb-like electric field, deriving the first law and exploring its thermodynamical properties, including special cases with zero cosmological constant.

Contribution

It introduces a thermodynamical interpretation of the field equations near the horizon for this specific black hole model.

Findings

Derived the differential form of the first law of thermodynamics for the black hole.

Showed the possibility of interpreting field equations thermodynamically near the horizon.

Analyzed the thermodynamics of the Lambda=0 solution.

Abstract

In this paper, we study the thermodynamical properties of the (2+1)dimensional black hole with a Coulomb-like electric field and the differential form of the first law of thermodynamics is derived considering a virtual displacement of its event horizon. This approach shows that it is possible to give a thermodynamical interpretation to the field equations near the horizon. The Lambda=0 solution is studied and its interesting thermodynamical properties are commented.