Casimir densities for two spherical branes in Rindler-like spacetimes

TL;DR

This paper calculates the vacuum expectation values and Casimir forces for a scalar field between two spherical branes in a Rindler-like spacetime, relevant to black hole near-horizon geometry, using the Abel-Plana formula.

Contribution

It provides explicit formulas for vacuum densities and Casimir forces in a higher-dimensional Rindler-like spacetime with spherical branes, including boundary condition effects.

Findings

Vacuum expectation values are expressed as sums of single and double brane contributions.

Interaction forces depend on brane positions and boundary conditions.

Limiting cases reveal behavior near horizons and large separations.

Abstract

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are evaluated for a scalar field obeying the Robin boundary conditions on two spherical branes in (D+1)-dimensional Rindler-like spacetime $Ri\times S^{D-1}$, with a two-dimensional Rindler spacetime $Ri$. This spacetime approximates the near horizon geometry of (D+1)-dimensional black hole. By using the generalized Abel-Plana formula, the vacuum expectation values are presented as the sum of single brane and second brane induced parts. Various limiting cases are studied. The vacuum forces acting on the branes are decomposed into the self-action and interaction terms. The interaction forces are investigated as functions of the brane locations and coefficients in the boundary conditions.