Quasi-Local Conserved Charges of Spin-3 Topologically Massive Gravity

TL;DR

This paper develops a quasi-local formalism to compute conserved charges and entropy for spin-3 topologically massive gravity, extending previous results and confirming consistency with black hole thermodynamics.

Contribution

It introduces a general formula for conserved charges and entropy in spin-3 topologically massive gravity, applicable to black hole solutions, and connects to known results in limiting cases.

Findings

Derived a universal formula for conserved charges in spin-3 topologically massive gravity.

Calculated energy, angular momentum, and entropy for a specific black hole solution.

Results are consistent with previous studies and the first law of black hole mechanics.

Abstract

In this paper we obtain conserved charges of spin-3 topologically massive gravity by using a quasi-local formalism. We find a general formula to calculate conserved charge of the spin-3 topologically massive gravity which corresponds to a Killing vector field $\xi$. We show that this general formula reduces to the previous one for the ordinary spin-3 gravity presented in \cite{31} when we take into account only transformation under diffeomorphism, without considering generalized Lorentz gauge transformation (i.e. $\lambda _{\xi} =0$), and by taking $\frac{1}{\mu}\rightarrow 0$. Then we obtain a general formula for the entropy of black hole solutions of the spin-3 topologically massive gravity. Finally we apply our formalism to calculate energy, angular momentum and entropy of a special black hole solution and we find that obtained results are consistent with previous results in the limiting cases. Moreover our result for energy, angular momentum and entropy are consistent with the first law of black hole mechanics.