Warped $AdS_3$ Black Hole in Minimal Massive Gravity with first order formalism

Soonkeon Nam, Jong-Dae Park

Published 2018-08-02Version 1

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 space-like warped $AdS_3$ black hole solution with some parameters conditions changing coordinates system into Schwarzschild one. Applying the Wald formalism to this theory with the first order formalism, we also find out entropy, mass and angular momentum of this black hole solution satisfying the first law of black hole thermodynamics. Under assumption that minimal massive gravity theory with suitable asymptotically warped $AdS_3$ boundary conditions is holographically dual to a 2-dimensional boundary CFT, we find appropriate central charges by using the relations between entropy of this black hole and the Cardy formula in dual CFT described by left and right moving central charges and temperatures.