Charged Rotating BTZ Black Hole and Thermodynamic Behavior of Field Equations at its Horizon

TL;DR

This paper investigates the properties of charged rotating BTZ black holes, deriving conditions for their horizons and demonstrating that Einstein's field equations at the horizon can be reformulated as the first law of thermodynamics.

Contribution

It provides a detailed analysis of the horizon conditions for charged rotating BTZ black holes and links Einstein's equations to thermodynamic laws at the horizon.

Findings

Derived conditions on mass, charge, and angular momentum for black hole horizons.

Expressed Einstein field equations at the horizon as the first law of thermodynamics.

Showed the thermodynamic interpretation of field equations at the black hole horizon.

Abstract

In this paper, we study different cases of the charged rotating BTZ black hole with reference to their horizons. For the existence of these cases conditions on mass, charge and angular momentum of the black hole are obtained. It is also shown that the Einstein field equations for the charged rotating BTZ black hole at the horizon can be expressed as first law of thermodynamics, $dE=TdS+\Omega dJ+\Phi dq+P_{r}dA$.