Casimir effect of two conducting parallel plates in a general weak gravitational field

Nazari, Borzoo

doi:10.1140/epjc/s10052-015-3732-y

Cited by 20 publications

(38 citation statements)

References 46 publications

(100 reference statements)

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“…Taking

κ_{1} = κ_{2} = 0

in for the Neumann or

β_{1} = β_{2} = 0

in for the Dirichlet conditions we find

\begin{matrix} true \\ right E = - (() 1 + γ_{0} + \frac{λ_{0} l_{p}}{2}) \frac{π^{2}}{1440 l_{p}^{3}} . \end{matrix}

This result is the same as (52) of for the energy of the Casimir effect in a general weak gravitational field under the Dirichlet and Neumann boundary conditions. For

γ_{0} = 0

, inspects (5.2) in, (5.4) in and (3.4) in).…”

Section: Consistency Of and With The Literaturesupporting

confidence: 76%

“…For some theories of gravity, the coefficients

γ_{0}, γ_{1}

and

λ_{0}, λ_{1}

are not necessarily equal. For other examples see . The mode frequencies inside the Casimir plates was shown to be

Ω = (1 + γ_{0}) ω

, where ω is the mode frequency for the same problem in the following (Fermi) spacetime:

\begin{matrix} true \\ right d s^{2} = (1 + 2 λ_{0} z) d t^{2} - d x^{2} - d y^{2} - d z^{2} . \end{matrix}

Thus, we first find ω for the Fermi spacetime under the Robin boundary conditions.…”

Section: Finding Mode Frequencies Inside the Plates For Robin Boundarmentioning

confidence: 97%

“…In, we have shown that inside the plates, any static, or under certain conditions, any slowly rotating stationary weak gravitational field can be described by the metric

\begin{matrix} true \\ right d s^{2} & = & left (1 + 2 γ_{0} + 2 λ_{0} z) d t^{2} - (1 + 2 γ_{1} + 2 λ_{1} z) \\ left false[d x^{2} + d y^{2} + d z^{2} false], \end{matrix}

in which

γ_{0}, λ_{0}, γ_{1}, λ_{1} < < 1

. For instance, if the source is the Earth and the apparatus is near the surface of the Earth, the distance is approximately the Earth's radius, i.e.,

R ≃ R_{E}

.…”

Section: Finding Mode Frequencies Inside the Plates For Robin Boundarmentioning

confidence: 99%

“…Although the Casimir effect under the Robin conditions have been previously studied in the flat spacetime, in curved spacetime, computation of the corrections to the energy and force has been concentrated mainly on the Dirichlet and Neumann boundary conditions . This is related to the fact that the Dirichlet and Neumann boundary conditions naturally arise for the electromagnetic Casimir effect in the presence of conducting spherical shells.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the calculations for the Robin problem are much more complicated than other types of conditions. Following our previous work we extend the calculation of the energy to a general weak gravitational field for the Robin conditions .…”

Section: Introductionmentioning

confidence: 99%

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Robin Boundary Condition for Casimir Plates in a General Weak Gravitational Field

Nazari

2017

Annalen der Physik

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The energy of the massless scalar field inside parallel Casimir plates in a general weak gravitational field under the influence of Robin boundary conditions is calculated. The mode frequencies are found in asymptotic limits and consistency of results with the literature is shown. Experimental evidence for detection of corrections is explored. Finding Mode Frequencies Inside the Plates for Robin Boundary ConditionsThe problem is to find mode frequencies of a scalar Klein-Gordon field inside an apparatus consisting of two conducting parallel plates in a general weak gravitational field under the influence of the Robin boundary conditions. The spacetime is dsecribed by the common spherical r, θ, φ coordinates. The plates are in a

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“…Taking

κ_{1} = κ_{2} = 0

in for the Neumann or

β_{1} = β_{2} = 0

in for the Dirichlet conditions we find

\begin{matrix} true \\ right E = - (() 1 + γ_{0} + \frac{λ_{0} l_{p}}{2}) \frac{π^{2}}{1440 l_{p}^{3}} . \end{matrix}

This result is the same as (52) of for the energy of the Casimir effect in a general weak gravitational field under the Dirichlet and Neumann boundary conditions. For

γ_{0} = 0

, inspects (5.2) in, (5.4) in and (3.4) in).…”

Section: Consistency Of and With The Literaturesupporting

confidence: 76%

“…For some theories of gravity, the coefficients

γ_{0}, γ_{1}

and

λ_{0}, λ_{1}

are not necessarily equal. For other examples see . The mode frequencies inside the Casimir plates was shown to be

Ω = (1 + γ_{0}) ω

, where ω is the mode frequency for the same problem in the following (Fermi) spacetime:

\begin{matrix} true \\ right d s^{2} = (1 + 2 λ_{0} z) d t^{2} - d x^{2} - d y^{2} - d z^{2} . \end{matrix}

Thus, we first find ω for the Fermi spacetime under the Robin boundary conditions.…”

Section: Finding Mode Frequencies Inside the Plates For Robin Boundarmentioning

confidence: 97%

“…In, we have shown that inside the plates, any static, or under certain conditions, any slowly rotating stationary weak gravitational field can be described by the metric

\begin{matrix} true \\ right d s^{2} & = & left (1 + 2 γ_{0} + 2 λ_{0} z) d t^{2} - (1 + 2 γ_{1} + 2 λ_{1} z) \\ left false[d x^{2} + d y^{2} + d z^{2} false], \end{matrix}

in which

γ_{0}, λ_{0}, γ_{1}, λ_{1} < < 1

. For instance, if the source is the Earth and the apparatus is near the surface of the Earth, the distance is approximately the Earth's radius, i.e.,

R ≃ R_{E}

.…”

Section: Finding Mode Frequencies Inside the Plates For Robin Boundarmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robin Boundary Condition for Casimir Plates in a General Weak Gravitational Field

Nazari

2017

Annalen der Physik

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Theoretical analysis of Casimir and thermal Casimir effect in stationary space–time

Zhang

2017

Physics Letters B

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We investigate Casimir effect as well as thermal Casimir effect for a pair of parallel perfectly plates placed in general stationary space-time background. It is found that the Casimir energy is influenced by the 00-component of metric and the corresponding quantity in dragging frame. We give a scheme to renormalize thermal correction to free energy in curved space-time. It is shown that the thermal corrections to Casimir thermodynamic quantities not only depend on the proper temperature and proper geometrical parameters of the plates, but also on the determinant of space-time metric.

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A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation

et al. 2020

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Casimir effect of two conducting parallel plates in a general weak gravitational field

Cited by 20 publications

References 46 publications

Robin Boundary Condition for Casimir Plates in a General Weak Gravitational Field

Robin Boundary Condition for Casimir Plates in a General Weak Gravitational Field

Theoretical analysis of Casimir and thermal Casimir effect in stationary space–time

A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation

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