Casimir energy in the Fulling-Rindler vacuum

Saharian, A. A.; Davtyan, R. S.; Yeranyan, Armen

doi:10.1103/physrevd.69.085002

Cited by 66 publications

(97 citation statements)

References 39 publications

(74 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result exactly agrees with that found by Saharian et al [17] for Dirichlet, Neumann, and perfectly conducting plates for the finite Casimir interaction energy. The acceleration of Dirichlet plates follows from our result when the strong coupling limit λ → ∞ is taken.…”

Section: Discussionsupporting

confidence: 92%

How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy

Milton¹,

Parashar²,

Shajesh³

et al. 2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

It has been demonstrated that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. We here add further support to this conclusion by considering parallel semitransparent plates, that is, δ-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates (τ, x, y, ξ). Fixed ξ in such a spacetime represents uniform acceleration. We calculate the force on systems consisting of one or two such plates at fixed values of ξ. In the limit of large Rindler coordinate ξ (small acceleration), we recover (via the equivalence principle) the situation of weak gravity, and find that the gravitational force on the system is just M g, where g is the gravitational acceleration and M is the total mass of the system, consisting of the mass of the plates renormalized by the Casimir energy of each plate separately, plus the energy of the Casimir interaction between the plates. This reproduces the previous result in the limit as the coupling to the δ-function potential approaches infinity.

show abstract

Section: Discussionsupporting

confidence: 92%

How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy

Milton¹,

Parashar²,

Shajesh³

et al. 2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…For the geometry under consideration one has (no summation over p) R .1) we have used the expression for the energy-momentum tensor for a scalar field, which differs from the standard one by the term which vanishes on the solutions of the field equation and does not contribute to the boundary-induced vacuum expectation value (see Ref. [60]). …”

Section: Energy-momentum Tensormentioning

confidence: 99%

“…In the general case of bulk and boundary geometries the expression for the latter is given in Ref. [60] (see also the discussion in Ref. [63][64][65][66]).…”

Section: Energy-momentum Tensormentioning

confidence: 99%

Wightman function and the Casimir effect for a Robin sphere in a constant curvature space

2014

Self Cite

View full text Add to dashboard Cite

We evaluate the Wightman function, the mean field squared and the vacuum expectation value of the energy-momentum tensor for a scalar field with the Robin boundary condition on a spherical shell in the background of a constant negative curvature space. For the coefficient in the boundary condition there is a critical value above which the scalar vacuum becomes unstable. In both the interior and the exterior regions, the vacuum expectation values are decomposed into the boundary-free and sphere-induced contributions. For the latter, rapidly convergent integral representations are provided. In the region inside the sphere, the eigenvalues are expressed in terms of the zeros of the combination of the associated Legendre function and its derivative and the decomposition is achieved by making use of the Abel-Plana type summation formula for the series over these zeros. The sphere-induced contribution to the vacuum expectation value of the field squared is negative for the Dirichlet boundary condition and positive for the Neumann one. At distances from the sphere larger than the curvature scale of the background space the suppression of the vacuum fluctuations in the gravitational field corresponding to the negative curvature space is stronger compared with the case of the Minkowskian bulk. In particular, the decay of the vacuum expectation values with the distance is exponential for both massive and massless fields. The corresponding results are generalized for spaces with spherical bubbles and for cosmological models with negative curvature spaces.

show abstract

“…Note that in this formula we have used the form of the metric energy-momentum tensor which differs from the standard one by the term which vanishes for the solutions of the field equation (see, for instance, [47]). As in the case of the field square, for points away from the boundaries the renormalization is realized by subtracting the part corresponding to the Minkowski spacetime without boundaries.…”

Section: Vacuum Energy-momentum Tensormentioning

confidence: 99%

Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries

Saharian

Tarloyan

2008

Annals of Physics

View full text Add to dashboard Cite

Wightman function, the vacuum expectation values of the field square and the energymomentum tensor are investigated for a massive scalar field with general curvature coupling parameter inside a wedge with two coaxial cylindrical boundaries. It is assumed that the field obeys Dirichlet boundary condition on bounding surfaces. The application of a variant of the generalized Abel-Plana formula enables to extract from the expectation values the contribution corresponding to the geometry of a wedge with a single shell and to present the interference part in terms of exponentially convergent integrals. The local properties of the vacuum are investigated in various asymptotic regions of the parameters. The vacuum forces acting on the boundaries are presented as the sum of self-action and interaction terms. It is shown that the interaction forces between the separate parts of the boundary are always attractive. The generalization to the case of a scalar field with Neumann boundary condition is discussed.

show abstract

Casimir energy in the Fulling-Rindler vacuum

Cited by 66 publications

References 39 publications

How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy

How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy

Wightman function and the Casimir effect for a Robin sphere in a constant curvature space

Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries

Contact Info

Product

Resources

About