Near Horizon Symmetries of the Non-Extremal Black Hole Solutions of Generalized Minimal Massive Gravity

TL;DR

This paper investigates near horizon symmetries of non-extremal black holes within the Generalized Minimal Massive Gravity framework, deriving conserved charges, their algebra, and connections to black hole thermodynamics.

Contribution

It demonstrates that solutions of Einstein gravity with negative cosmological constants also solve GMMG equations and derives the algebra of near horizon conserved charges, including their physical interpretations.

Findings

Conserved charges form a centrally extended algebra.

Charge associated with rotations matches angular momentum.

Charge related to time translations equals entropy times temperature.

Abstract

We consider the Generalized Minimal Massive Gravity (GMMG) model in the first order formalism. We show that all the solutions of the Einstein gravity with negative cosmological constants solve the equations of motion of considered model. Then we find an expression for the off-shell conserved charges of this model. By considering the near horizon geometry of a three dimensional black hole in the Gaussian null coordinates, we find near horizon conserved charges and their algebra. The obtained algebra is centrally extended. By writing the algebra of conserved charges in terms of Fourier modes and considering the BTZ black hole solution as an example, one can see that the charge associated with rotations along $\mathcal{Y}_{0}$ coincides exactly with the angular momentum, and he charge associated with time translations $\mathcal{T}_{0}$ is the product of the black hole entropy and its temperature. As we expect, in the limit when the GMMG tends to the Einstein gravity, all the result we obtain in this paper reduce to the result of the paper \cite{5}.