Surface Casimir densities on a spherical brane in Rindler-like spacetimes

TL;DR

This paper calculates the vacuum surface energy-momentum tensor for a scalar field on a spherical brane in a Rindler-like spacetime, revealing finite energies in odd dimensions and linking to cosmological constant issues.

Contribution

It provides analytic expressions for surface energies on a spherical brane in higher-dimensional Rindler-like spacetime using zeta function techniques, including pole cancellation in odd dimensions.

Findings

Surface energies contain pole and finite parts, with poles canceling in odd dimensions.

Total surface energy is finite for an infinitely thin brane in odd spatial dimensions.

Surface energy-momentum tensor acts as a source of the cosmological constant.

Abstract

The vacuum expectation value of the surface energy-momentum tensor is evaluated for a scalar field obeying Robin boundary condition on a spherical brane in (D+1)-dimensional spacetime $Ri\times S^{D-1}$, where $Ri$ is a two-dimensional Rindler spacetime. The generalized zeta function technique is used in combination with the contour integral representation. The surface energies on separate sides of the brane contain pole and finite contributions. Analytic expressions for both these contributions are derived. For an infinitely thin brane in odd spatial dimensions, the pole parts cancel and the total surface energy, evaluated as the sum of the energies on separate sides, is finite. For a minimally coupled scalar field the surface energy-momentum tensor corresponds to the source of the cosmological constant type.