Warped AdS_3 black holes in new massive gravity

TL;DR

The paper demonstrates that cosmological $NMG$ in three dimensions admits both BTZ and warped $AdS_3$ black holes under a two-Killing-vector reduction. It derives the reduced equations with a conserved angular momentum and reduces the problem to algebraic conditions that yield explicit BTZ and warped $AdS_3$ metrics, including a causal regularity regime and an $AdS_2\times S^1$ solution at $\Lambda = m^2$. Entropy, mass and angular momentum are computed using Wald's formula and an extended ADT framework, revealing a simple entropy renormalization for warped $AdS_3$ and a consistent first law and Smarr relation for both black hole families. The results provide a thermodynamically consistent picture of warped black holes in $NMG$ and motivate further foundational work on energy signs and ADT in non-constant-curvature backgrounds.

Abstract

We investigate stationary, rotationally symmetric solutions of a recently proposed three-dimensional theory of massive gravity. Along with BTZ black holes, we also obtain warped AdS_3 black holes, and (for a critical value of the cosmological constant) AdS_2 x S^1 as solutions. The entropy, mass and angular momentum of these black holes are computed.