Casimir densities for two spherical branes in Rindler-like spacetimes

Saharian, A. A.; Setare, M. R.

doi:10.1088/1126-6708/2007/02/089

Cited by 10 publications

(7 citation statements)

References 68 publications

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“…In this limit the black hole geometry may be approximated by the Rindler-like manifold (for some investigations of quantum effects on background of Rindler-like spacetimes see [143,144] and references therein). In this section, by using the GAPF, we investigate the Wightman function, the VEVs of the field square and the EMT for a scalar field with an arbitrary curvature coupling parameter for two spherical branes in the bulk Ri × S D−1 , where Ri is a two-dimensional Rindler spacetime [58].…”

Section: Casimir Densities For Spherical Branes In Rindler-like Space...mentioning

confidence: 99%

“…( 21 (int) > 0 and the interaction forces are repulsive for all distances between the branes. The investigation of the vacuum densities in various asymptotic regions of the parameters can be forund in [58,144].…”

Section: Vacuum Densitiesmentioning

confidence: 99%

“…The corresponding mode-sums for physical observables bilinear in the field contain series over the zeroes of cylinder functions which are summarized by using the generalized Abel-Plana formula. The geometry of spherical branes in Rindler-like spacetimes is considered in [58]. In [59] from the generalized Abel-Plana formula a summation formula is derived over the eigenmodes of a dielectric cylinder and this formula is applied for the evaluation of the radiation intensity from a point charge orbiting along a helical trajectory inside the cylinder.…”

Section: Introductionmentioning

confidence: 99%

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The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect

Saharian

2007

Preprint

110

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One of the most efficient methods for the evaluation of the vacuum expectation values for physical observables in the Casimir effect is based on using the Abel-Plana summation formula. This enables to derive the renormalized quantities in a manifestly cutoff independent way and to present them in the form of strongly convergent integrals. However, applications of the Abel-Plana formula, in its usual form, are restricted by simple geometries when the eigenmodes have a simple dependence on quantum numbers. The author generalized the Abel-Plana formula which essentially enlarges its application range. Based on this generalization, formulae have been obtained for various types of series over the zeros of combinations of Bessel functions and for integrals involving these functions. It has been shown that these results generalize the special cases existing in literature. Further, the derived summation formulae have been used to summarize series arising in the direct mode summation approach to the Casimir effect for spherically and cylindrically symmetric boundaries, for boundaries moving with uniform proper acceleration, and in various braneworld scenarios. This allows to extract from the vacuum expectation values of local physical observables the parts corresponding to the geometry without boundaries and to present the boundary-induced parts in terms of integrals strongly convergent for the points away from the boundaries. As a result, the renormalization procedure for these observables is reduced to the corresponding procedure for bulks without boundaries. The present paper reviews these results. We also aim to collect the results on vacuum expectation values for local physical observables such as the field square and the energy-momentum tensor in manifolds with boundaries for various bulk and boundary geometries.

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Section: Casimir Densities For Spherical Branes In Rindler-like Space...mentioning

confidence: 99%

Section: Vacuum Densitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect

Saharian

2007

Preprint

110

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“…The use of Casimir effect in stabilizing extra dimensions were considered in [16,17,18,19,20,21,22,23,24,25]. In the braneworld scenario, Casimir effect was also considered in [26,27,28,29,30,31,32,33,34]. The influence of the extra dimensions on the Casimir force acting on a pair of parallel plates in macroscopic (3+1)-dimensional spacetime was studied in [13,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50].…”

Section: Introductionmentioning

confidence: 99%

Casimir effect in spacetime with extra dimensions – from Kaluza–Klein to Randall–Sundrum models

Teo¹

2009

Physics Letters B

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In this article, we derive the finite temperature Casimir force acting on a pair of parallel plates due to a massless scalar field propagating in the bulk of a higher dimensional brane model. In contrast to previous works which used approximations for the effective masses in deriving the Casimir force, the formulas of the Casimir force we derive are exact formulas. Our results disprove the speculations that existence of the warped extra dimension can change the sign of the Casimir force, be it at zero or any finite temperature.

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“…For Randall-Sundrum spacetime model [20,21], Robin boundary conditions are natural for scalar fields and fermion fields, where the Robin coefficients are related to the curvature scale and the boundary mass terms of the fields [22,23,24,25]. Casimir effect in braneworld models with Robin boundary conditions on the branes was discussed extensively in [25,26,27,28,29,30,31,32,33,34,35,36,37].…”

Section: Introductionmentioning

confidence: 99%

Finite temperature Casimir effect for scalar field with Robin boundary conditions in spacetime with extra dimensions

Teo¹

2009

J. High Energy Phys.

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In this article, we study the finite temperature Casimir effect for scalar field with Robin boundary conditions on two parallel plates in a background spacetime that has a compact internal manifold with arbitrary geometry. The finite temperature Casimir force acting on the plates is derived using the piston approach, with which we show that the divergences of the Casimir forces from the region between the plates and the region outside the plates cancel each other. The sign and asymptotic behaviors of the Casimir force at different limits such as small and large plate separation, low and high temperature, are studied in detail. The range of Robin coefficients where the Casimir force are always attractive or always repulsive are determined. There are also some range of the Robin coefficients where the Casimir force is shown to be attractive at small plate separation and repulsive at large plate separation, or vise versa.

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Casimir densities for two spherical branes in Rindler-like spacetimes

Cited by 10 publications

References 68 publications

The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect

The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect

Casimir effect in spacetime with extra dimensions – from Kaluza–Klein to Randall–Sundrum models

Finite temperature Casimir effect for scalar field with Robin boundary conditions in spacetime with extra dimensions

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