Microscopic entropy of the three-dimensional rotating black hole of BHT massive gravity

TL;DR

The paper analyzes a three-dimensional rotating black hole in BHT massive gravity, introducing a gravitational hair parameter that yields a negative mass bound and an extremal ground state with vanishing temperature and entropy. It shows that the first law can absorb variations of the hair parameter through shifts in the global charges, supporting M0 as the ground state. By employing relaxed AdS3 boundary conditions and Cardy’s formula with c± = 3l/G, the authors reproduce the semiclassical entropy from microscopic states, confirming a consistent AdS3/CFT2 interpretation. The work also discusses the role of the gravitational hair in extremality and notes possible ground-state candidates (solitons) for b>0, with extensions to special parameter choices. Overall, it provides a coherent thermodynamic and microscopic picture for these BHT rotating black holes.

Abstract

Asymptotically AdS rotating black holes for the Bergshoeff-Hohm-Townsend (BHT) massive gravity theory in three dimensions are considered. In the special case when the theory admits a unique maximally symmetric solution, apart from the mass and the angular momentum, the black hole is described by an independent "gravitational hair" parameter, which provides a negative lower bound for the mass. This bound is saturated at the extremal case and, since the temperature and the semiclassical entropy vanish, it is naturally regarded as the ground state. The absence of a global charge associated with the gravitational hair parameter reflects through the first law of thermodynamics in the fact that the variation of this parameter can be consistently reabsorbed by a shift of the global charges, giving further support to consider the extremal case as the ground state. The rotating black hole fits within relaxed asymptotic conditions as compared with the ones of Brown and Henneaux, such that they are invariant under the standard asymptotic symmetries spanned by two copies of the Virasoro generators, and the algebra of the conserved charges acquires a central extension. Then it is shown that Strominger's holographic computation for general relativity can also be extended to the BHT theory; i.e., assuming that the quantum theory could be consistently described by a dual conformal field theory at the boundary, the black hole entropy can be microscopically computed from the asymptotic growth of the number of states according to Cardy's formula, in exact agreement with the semiclassical result.