Vacuum polarization on the brane

Abstract

We compute the renormalized expectation value of the square of a massless, conformally coupled, quantum scalar field on the brane of a higher-dimensional black hole. Working in the AADD brane-world scenario, the extra dimensions are flat and we assume that the compactification radius is large compared with the size of the black hole. The four-dimensional on-brane metric corresponds to a slice through a higher-dimensional Schwarzschild-Tangherlini black hole geometry and depends on the number of bulk space-time dimensions. The quantum scalar field is in a thermal state at the Hawking temperature. An exact, closed-form expression is derived for the renormalized expectation value of the square of the quantum scalar field on the event horizon of the black hole. Outside the event horizon, this renormalized expectation value is computed numerically. The answer depends on the number of bulk space-time dimensions, with a magnitude which increases rapidly as the number of bulk space-time dimensions increases.

17 pages, 4 figures, minor changes, accepted for publication in Physical Review D

References in corpus (11)

• BlackMax: A black-hole event generator with rotation, recoil, split branes and brane tension
• Black Holes at the LHC
• Vacuum polarization for lukewarm black holes
• Hawking Radiation from Higher-Dimensional Black Holes
• Pade Approximants of the Green Function in Spherically Symmetric Spacetimes
• Vacuum polarization in asymptotically anti-de Sitter black hole geometries
• DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions
• Vacuum Polarization on the Schwarzschild Metric with a Cosmic String
• Renormalized Vacuum Polarization and Stress Tensor on the Horizon of a Schwarzschild Black Hole Threaded by a Cosmic String
• Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes
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Cited by in corpus (7)

• Versatile method for renormalized stress-energy computation in black-hole spacetimes
• A Mode-Sum Prescription for Vacuum Polarization in Odd Dimensions
• Vacuum polarization on topological black holes with Robin boundary conditions
• Vacuum polarization in asymptotically Lifshitz black holes
• 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