Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity

TL;DR

This paper demonstrates that warped AdS3 black holes are solutions in generalized minimal massive gravity, analyzes their asymptotic symmetries, and confirms the consistency of their thermodynamics with a dual warped conformal field theory.

Contribution

It introduces boundary conditions for warped AdS3 in GMMG, computes conserved charges, and establishes the dual warped CFT description with matching entropy.

Findings

Warped AdS3 black holes are solutions in GMMG.

The asymptotic symmetry algebra is a semi-direct product of Virasoro and U(1).

Black hole entropy matches the Cardy formula.

Abstract

In this paper we show that warped AdS$_{3}$ black hole spacetime is a solution of the generalized minimal massive gravity (GMMG) and introduce suitable boundary conditions for asymptotically warped AdS$_{3}$ spacetimes. Then we find the Killing vector fields such that transformations generated by them preserve the considered boundary conditions. We calculate the conserved charges which correspond to the obtained Killing vector fields and show that the algebra of the asymptotic conserved charges is given as the semi direct product of the Virasoro algebra with $U(1)$ current algebra. We use a particular Sugawara construction to reconstruct the conformal algebra. Thus, we are allowed to use the Cardy formula to calculate the entropy of the warped black hole. We demonstrate that the gravitational entropy of the warped black hole exactly coincide with what we obtain via Cardy's formula. As we expect the warped Cardy formula also give us exactly the same result which we obtain from usual Cardy's formula. We calculate mass and angular momentum of the warped black and then check that obtained mass, angular momentum and entropy satisfy first law of the black hole mechanics. According to the results of this paper we belief that the dual theory of the warped AdS$_{3}$ black hole solution of GMMG is a Warped CFT.