Casimir densities for a spherical brane 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 mixed boundary condition on a spherical brane in (D+1)-dimensional Rindler-like spacetime $Ri\times S^{D-1}$, where $Ri$ is a two-dimensional Rindler spacetime. This spacetime approximates the near horizon geometry of (D+1) -dimensional black hole in the large mass limit. The vacuum expectation values are presented as the sum of boundary-free and brane-induced parts. Further we extract from the Wightman function for the boundary-free geometry the corresponding function in the bulk $R^2\times S^{D-1}$. For the latter geometry the vacuum expectation values of the field square and the energy-momentum tensor do not depend on the spacetime point. For the renormalization of these quantities we use zeta regularization technique. Various limiting cases of the brane-induced vacuum expectation values are investigated.

15 pages, Application to the AdS black hole braneworld and references added, accepted for publication in Nuclear Physics B

References in corpus (4)

• Surface Casimir densities and induced cosmological constant on parallel branes in AdS
• Stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum brane model
• Bouncing Cosmologies and Self-Gravitational Corrections
• Quantum Fluctuations for de Sitter Branes in Bulk AdS(5)

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