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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.
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