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

Understand

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.