Surface Casimir densities on branes orthogonal to the boundary of
anti-de Sitter spacetime
- URL: http://arxiv.org/abs/2309.06408v2
- Date: Sun, 21 Jan 2024 15:19:06 GMT
- Title: Surface Casimir densities on branes orthogonal to the boundary of
anti-de Sitter spacetime
- Authors: A. A. Saharian
- Abstract summary: We investigate the vacuum expectation value of the surface energy-momentum tensor (SEMT) for a scalar field with general curvature coupling.
For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes.
The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We investigate the vacuum expectation value of the surface energy-momentum
tensor (SEMT) for a scalar field with general curvature coupling in the
geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS)
spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed
into the contributions corresponding to the self-energies of the branes and the
parts induced by the presence of the second brane. The renormalization is
required for the first parts only and for the corresponding regularization the
generalized zeta function method is employed. The induced SEMT is finite and is
free from renormalization umbiguities. For an observer living on the brane, the
corresponding equation of state is of the cosmological constant type. Depending
on the boundary conditions and on the separation between the branes, the
surface energy densities can be either positive or negative. The energy density
induced on the brane vanishes in special cases of Dirichlet and Neumann
boundary conditions on that brane. The effect of gravity on the induced SEMT is
essential at separations between the branes of the order or larger than the
curvature radius for AdS spacetime. In the large separation limit the decay of
the SEMT, as a function of the proper separation, follows a power law for both
massless and massive fields. For parallel plates in Minkowski bulk and for
massive fields the fall-off of the corresponding expectation value is
exponential.
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