Casimir densities for two spherical branes in Rindler-like spacetimes

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.

15 pages

References in corpus (4)

• Surface Casimir densities and induced cosmological constant in higher dimensional braneworlds
• Stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum brane model
• Surface Casimir densities on a spherical brane in Rindler-like spacetimes
• Bouncing cosmological solutions due to the self-gravitational corrections and their stability

Cited by in corpus (8)

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• The Casimir densities for a sphere in the Milne universe
• Summation formula over the zeros of the associated Legendre function with a physical application
• Casimir densities for a boundary in Robertson-Walker spacetime
• Vacuum densities for a thick brane in AdS spacetime