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

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.