Quantum Kerr-de Sitter black holes in three dimensions

We use braneworld holography to construct a three-dimensional quantum-corrected Kerr-de Sitter black hole, exactly accounting for semi-classical backreaction effects due to a holographic conformal field theory. By contrast, classically there are no de Sitter black holes in three-dimensions, only geometries with a single cosmological horizon. The quantum Kerr black hole shares many qualitative features with the classical four-dimensional Kerr-de Sitter solution. Of note, backreaction induces inner and outer black hole horizons which hide a ring singularity. Moreover, the quantum-corrected geometry has extremal, Nariai, and ultracold limits, which appear as fibered products of a circle and two-dimensional anti-de Sitter, de Sitter, and Minkowski space, respectively. The thermodynamics of the classical bulk black hole, described by the rotating four-dimensional anti-de Sitter C-metric, has an interpretation on the brane as thermodynamics of the quantum black hole, obeying a semi-classical first law where the Bekenstein-Hawking area entropy is replaced by the generalized entropy. For purposes of comparison, we derive the renormalized quantum stress-tensor due to a free conformally coupled scalar field in the classical Kerr-de Sitter conical geometry and perturbatively solve for its backreaction.