Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-09-11
Phys.Rev. D59 (1999) 104017
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages, RevTeX, no figures, minor changes, final version accepted for publication in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.59.104017
The behavior of a quantum scalar field is studied in the metric ground state of the (2+1)-dimensional black hole of Ba\~nados, 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.
Binosi Daniele
Moretti Valter
Vanzo Luciano
Zerbini Sergio
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