Vacuum densities for a thick brane in AdS spacetime

TL;DR

This paper calculates vacuum densities and energy-momentum tensor for a scalar field in a thick brane within AdS spacetime, revealing how brane properties influence quantum vacuum effects and brane stability.

Contribution

It provides a comprehensive analysis of vacuum expectation values for a scalar field in a thick brane scenario in AdS space, including a specific Minkowski interior model.

Findings

Vacuum expectation values are split into free AdS and brane-induced parts.

For conformally coupled massless scalar, brane-induced vacuum energy-momentum vanishes.

Vacuum forces tend to decrease the brane thickness.

Abstract

For a massive scalar field with general curvature coupling parameter we evaluate Wightman function, vacuum expectation values of the field square and the energy-momentum tensor induced by a $Z_{2}$-symmetric brane with finite thickness located on $(D+1)$-dimensional AdS bulk. For the general case of static plane symmetric interior structure the expectation values in the region outside the brane are presented as the sum of free AdS and brane induced parts. For a conformally coupled massless scalar the brane induced part in the vacuum energy-momentum tensor vanishes. In the limit of strong gravitational fields the brane induced parts are exponentially suppressed for points not too close to the brane boundary. As an application of general results a special model is considered in which the geometry inside the brane is a slice of the Minkowski spacetime orbifolded along the direction perpendicular to the brane. For this model the Wightman function, vacuum expectation values of the field square and the energy-momentum tensor inside the brane are evaluated. It is shown that for both minimally and conformally coupled scalar fields the interior vacuum forces acting on the brane boundaries tend to decrease the brane thickness.