Boundary Conditions of Warped AdS$_3$ in New Massive Gravity

Abstract: To satisfy the Cardy formula for Warped AdS$3$ (WAdS${3}$) solutions in a quadratic ensemble, a specific set of boundary conditions has been proposed in \cite{Aggarwal:2020igb}. In this paper, these boundary conditions have been investigated in the three-dimensional new massive gravity (NMG) framework. The associated solution space, asymptotic symmetries, and charge algebra have been extracted. It has been shown that the surface charges are finite, but not integrable, and the integrability of the charges is obtained after restricting to a sub-sector of the original solution space. Finally, we have proved that the Cardy formula reproduces the thermodynamic entropy of a warped BTZ black hole.