#### Document Type

Article

#### Rights

This item is available under a Creative Commons License for non-commercial use only

#### Disciplines

Applied mathematics, Particles and fields physics

#### 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 braneworld 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.

#### Recommended Citation

Breen, C., et al. (2015) Vacuum Polarization on the Brane, Physical Review D, http://arxiv.org/abs/1507.05026

## Publication Details

Accepted for Publication in Physical Review D