Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background

Abstract

The behavior of a quantum scalar field is studied in the metric ground state of the (2+1)-dimensional black hole of Bañados, Teitelboim and Zanelli which contains a naked singularity. The one-loop BTZ partition function and the associate black hole effective entropy, the expectation value of the quantum fluctuation as well as the renormalized expectation value of the stress tensor are explicitly computed in the framework of the $\zeta$-function procedure. This is done for all values of the coupling with the curvature, the mass of the field and the temperature of the quantum state. In the massless conformally coupled case, the found stress tensor is used for determining the quantum back reaction on the metric due to the scalar field in the quantum vacuum state, by solving the semiclassical Einstein equations. It is finally argued that, within the framework of the 1/N expansion, the Cosmic Censorship Hypothesis is implemented since the naked singularity of the ground state metric is shielded by an event horizon created by the back reaction.

18 pages, RevTeX, no figures, minor changes, final version accepted for publication in Phys. Rev. D

References in corpus (11)

• Black holes with unusual topology
• What We Don't Know about BTZ Black Hole Entropy
• Black Holes of Negative Mass
• Local $\zeta$-function techniques vs point-splitting procedure: a few rigorous results
• Quantum fluctuation of stress tensor and black holes in three dimensions
• One-loop stress-tensor renormalization in curved background: the relation between $\zeta$-function and point-splitting approaches, and an improved point-splitting procedure
• Quantum Correction to the Entropy of the (2+1)-Dimensional Black Hole
• Can Quantum-Corrected BTZ Black Hole Anti-Evaporate?
• zeta-function regularization and one-loop renormalization of field fluctuations in curved space-times
• Quantization of Black Holes in the Wheeler-DeWitt Approach
• Quantum implementation of the cosmic censorship conjecture for toroidal black holes

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• Dissipative dynamics of an open quantum battery in the BTZ spacetime
• Vacuum polarization on topological black holes with Robin boundary conditions
• Quantum gravitational corrections to the stress-energy tensor around the rotating BTZ black hole
• Quantum corrections for BTZ black hole via 2D reduced model
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Vacuum polarization on topological black holes
• The Lamb shift in the BTZ spacetime
• The effect of geometry on charge confinement in three dimensions