Quantum backreaction for overspinning BTZ geometries

Abstract

We examine the semiclassical backreaction of a conformally coupled scalar field on an overspinning BTZ geometry. This extends the work done on a similar problem for ($2+1$)- AdS geometries of the BTZ family with $|M|>|J|$. The overspinning classical solutions corresponds to $|M|<|J|$ and possess a naked singularity at $r=0$. Using the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such a spacetime, we obtain the semiclassical Einstein equations, which we attempt to solve perturbatively. We show that the stress-energy tensor is non-renormalizable in this approach, and consequently the perturbative solution to the semiclassical equations in the overspinning case does not exist. This could be an indication of the fact that the naked singularity at the center of an overspinning geometry is of a more severe nature than the conical singularity found in the same family of BTZ geometries.

References in corpus (12)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator
• Quantum BTZ black hole
• Birkhoff's Theorem for Three-Dimensional AdS Gravity
• On the negative spectrum of the 2+1 black hole
• Quantum fluctuation of stress tensor and black holes in three dimensions
• Quantum Backreaction on Three-Dimensional Black Holes and Naked Singularities
• Quantum dress for a naked singularity
• Quantum-corrected black holes and naked singularities in (2+1)-dimensions
• Vacuum polarization near asymptotically anti-de Sitter black holes in odd dimensions
• Overspinning naked singularities in AdS${}_3$ spacetime

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• Spinning Particle Geometries in AdS${}_3$/CFT${}_2$
• Renormalisation in maximally symmetric spaces and semiclassical gravity in Anti-de Sitter spacetime
• Nontrivial self-consistent backreaction of quantum fields in 2D dilaton gravity