Warped $AdS_3$ black hole in minimal massive gravity with first order formalism

TL;DR

This paper derives a warped $AdS_3$ black hole solution in minimal massive gravity using the first order formalism, analyzes its thermodynamics, and explores its holographic dual with computed central charges.

Contribution

It presents a new warped $AdS_3$ black hole solution in minimal massive gravity with first order formalism and establishes its thermodynamic and holographic properties.

Findings

Black hole solution satisfies first law of thermodynamics.

Entropy matches the Cardy formula predictions.

Central charges are explicitly computed for the dual CFT.

Abstract

We obtain a black hole solution of minimal massive gravity theory with Maxwell and electromagnetic Chern-Simons terms using the first order formalism. This black hole solution can be translated into the spacelike warped $AdS_3$ black hole solution with some parameters' conditions changing their coordinates system into a Schwarzschild one. Applying the Wald formalism to this theory with the first order formalism, we also find out the entropy, mass, and angular momentum of this black hole solution satisfies the first law of black hole thermodynamics. Under the assumption that minimal massive gravity theory with suitable asymptotically warped $AdS_3$ boundary conditions is holographically dual to a two dimensional boundary conformal field theory, we find appropriate central charges by using the relations between entropy of this black hole and the Cardy formula in dual conformal field theory described by left and right moving central charges and temperatures.