Quantum-corrected black holes and naked singularities in (2+1)-dimensions

Abstract

We analytically investigate the pertubative effects of a quantum conformally-coupled scalar field on rotating (2+1)-dimensional black holes and naked singularities. In both cases we obtain the quantum-backreacted metric analytically. In the black hole case, we explore the quantum corrections on different regions of relevance for a rotating black hole geometry. We find that the quantum effects lead to a growth of both the event horizon and the ergosphere, as well as to a reduction of the angular velocity compared to their corresponding unperturbed values. Quantum corrections also give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the naked singularity case, quantum effects lead to the formation of a horizon that hides the conical defect, thus turning it into a black hole. The fact that these effects occur not only for static but also for spinning geometries makes a strong case for the rôle of quantum mechanics as a cosmic censor in Nature.

46 pages, 12 figures

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• Semiclassical gravity with a conformally covariant field in globally hyperbolic spacetimes
• Renormalization of $⟨{\varphi }^2⟩$ at the inner horizon of rotating, accreting black holes
• Wave equations in conformally separable, accreting, rotating black holes
• Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell
• C-metric in a (nut)shell
• Timelike entanglement and central charge for quantum BTZ black holes