Vacuum polarization near asymptotically anti-de Sitter black holes in odd dimensions

Abstract

Recently, Bañados, Teitelboim and Zanelli obtained spherically symmetric black hole solutions in a particular class of Einstein--Lovelock gravity. We derive the propagator in an exact form for a conformal scalar field in the asymptotically anti-de Sitter black hole spacetime so as to study the quantum effects of the scalar fields. We treat the cases in odd dimensions in this paper. We calculate the vacuum expectation value of $⟨{\phi }^2⟩$ and show its dependence on the radial coordinate for the five-dimensional case as an example.

arXiv comment12 pages, 3 figures

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• Gravitational Effects of Quantum Fields in the Interior of a Cylindrical Black Hole
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• Vacuum polarization on the brane
• Vacuum polarization on topological black holes
• Black Hole Quantum Vacuum Polarization in Higher Dimensions
• Quantum vacuum polarization around a Reissner-Nordström black hole in five dimensions
• Classical and Quantum Thermodynamic Systems in Curved Spacetime