Remarks on a gravitational analogue of the Casimir effect

2016 ◽  
Vol 25 (09) ◽  
pp. 1641018 ◽  
Author(s):  
V. B. Bezerra ◽  
H. F. Mota ◽  
C. R. Muniz
Keyword(s):  
Scalar Field ◽  
Cosmic String ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
String Tension ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Einstein Universe

We consider the Casimir effect, by calculating the Casimir energy and its corrections for nonzero temperatures, of a massless scalar field in the spacetime with topology [Formula: see text] (Einstein universe) containing an idealized cosmic string. The obtained results confirm the role played by the identifications imposed on the quantum field by boundary conditions arising from the topology of the gravitational field under consideration and illustrate a realization of a gravitational analogue of the Casimir effect. In this backgorund, we show that the vacuum energy can be written as a term which corresponds to the vacuum energy of the massless scalar field in the Einstein universe added by another term that formally corresponds to the vacuum energy of the electromagnetic field in the Einstein universe, multiplied by a parameter associated with the presence of the cosmic string, namely, [Formula: see text], where [Formula: see text] is a constant related to the cosmic string tension, [Formula: see text].

Thermal Casimir effect in the Kerr spacetime with quintessence

2019 ◽  
Vol 34 (16) ◽  
pp. 1950125
Author(s):  
V. B. Bezerra ◽  
J. M. Toledo
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Equatorial Plane ◽  
Casimir Effect ◽  
Kerr Black Hole ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Kerr Spacetime

We calculate thermal corrections to the Casimir energy of a massless scalar field in the Kerr black hole surrounded by quintessence, taking into account the metrics derived by Ghosh [S. G. Ghosh, Eur. Phys. J. C 76, 222 (2016)] and Toshmatov et al. [B. Toshmatov, Z. Stuchlík and B. Ahmedov, Eur. Phys. J. Plus 132, 98 (2017)]. We compare both results and show that they are almost the same, except very close to the horizons. At [Formula: see text], equatorial plane, the results are the same, as should be expected, due to the fact that the metrics coincide in this region.

scholarly journals SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC SPHERES

2012 ◽  
Vol 27 (16) ◽  
pp. 1250082 ◽  
Author(s):  
MUSTAFA ÖZCAN
Keyword(s):  
Scalar Field ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Outer Radius ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
New Approach ◽  
Concentric Spheres ◽  
Spherical Boundary

The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We developed a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions. The Casimir energy for a massless scalar field between the closely spaced two concentric spheres coincides with the Casimir energy of the parallel plates for a massless scalar field in the limit when the dimensionless parameter η, ([Formula: see text] where a(b) is inner (outer) radius of sphere), goes to zero. The efficiency of new approach is demonstrated by calculation of the Casimir energy for a massless scalar field between the closely spaced two concentric half spheres.

scholarly journals Comments on “Casimir effect in the Kerr spacetime with quintessence”

2017 ◽  
Vol 32 (21) ◽  
pp. 1775001 ◽  
Author(s):  
Bobir Toshmatov ◽  
Zdeněk Stuchlík ◽  
Bobomurat Ahmedov
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Casimir Effect ◽  
Kerr Black Hole ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Kerr Spacetime ◽  
The Difference

This comment is devoted to the recalculation of the Casimir energy of a massless scalar field in the Kerr black hole surrounded by quintessence derived in [B. Toshmatov, Z. Stuchlík and B. Ahmedov, Eur. Phys. J. Plus 132, 98 (2017)] and its comparison with the results recently obtained in [V. B. Bezerra, M. S. Cunha, L. F. F. Freitas and C. R. Muniz, Mod. Phys. Lett. A 32, 1750005 (2017)] in the spacetime [S. G. Ghosh, Eur. Phys. J. C 76, 222 (2016)]. We have shown that in the more realistic spacetime which does not have the failures illustrated here, the Casimir energy is significantly bigger than that derived in [V. B. Bezerra, M. S. Cunha, L. F. F. Freitas and C. R. Muniz, Mod. Phys. Lett. A 32, 1750005 (2017)], and the difference becomes crucial especially in the regions of near horizons of the spacetime.

scholarly journals Remarks on Some Results Related to the Thermal Casimir Effect in Einstein and Closed Friedmann Universes with a Cosmic String

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 232
Author(s):  
Valdir Barbosa Bezerra ◽  
Herondy Francisco Santana Mota ◽  
Celio Rodrigues Muniz ◽  
Carlos Augusto Romero Filho
Keyword(s):  
Free Energy ◽  
Scalar Field ◽  
Internal Energy ◽  
Cosmic String ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Thermodynamic Quantities ◽  
Spinor Fields ◽  
Massless Spinor

In this paper, we present a review of some recent results concerning the thermal corrections to the Casimir energy of massless scalar, electromagnetic, and massless spinor fields in the Einstein and closed Friedmann universes with a cosmic string. In the case of a massless scalar field, it is shown that the Casimir energy can be written as a simple sum of two terms; the first one corresponds to the Casimir energy for the massless scalar field in the Einstein and Friedmann universes without a cosmic string, whereas the second one is simply the Casimir energy of the electromagnetic in this background, multiplied by a parameter λ=(1/α)−1, where α is a constant that codifies the presence of the cosmic string, and is related to its linear mass density, μ, by the expression α=1−Gμ. The Casimir free energy and the internal energy at a temperature different from zero, as well as the Casimir entropy, are given by similar sums. In the cases of the electromagnetic and massless spinor fields, the Casimir energy, free energy, internal energy, and Casimir entropy are also given by the sum of two terms, similarly to the previous cases, but now with both terms related to the same field. Using the results obtained concerning the mentioned thermodynamic quantities, their behavior at high and low temperatures limits are studied. All these results are particularized to the scenario in which the cosmic string is absent. Some discussions concerning the validity of the Nernst heat theorem are included as well.

scholarly journals SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC D-DIMENSIONAL SPHERES

2012 ◽  
Vol 27 (18) ◽  
pp. 1250094 ◽  
Author(s):  
MUSTAFA ÖZCAN
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Complex Plane ◽  
Casimir Force ◽  
Dirichlet Boundary ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Dirichlet Boundary Conditions ◽  
Massless Scalar ◽  
Massless Scalar Field

The Casimir energy for a massless scalar field between the closely spaced two concentric D-dimensional (for D>3) spheres is calculated by using the mode summation with contour integration in the complex plane of eigenfrequencies and the generalized Abel–Plana formula for evenly spaced eigenfrequency at large argument. The sign of the Casimir energy between closely spaced two concentric D-dimensional spheres for a massless scalar field satisfying the Dirichlet boundary conditions is strictly negative. The Casimir energy between (D-1)-dimensional surfaces, close to each other is regarded as interesting both by itself and as the key to describing of stability of the attractive Casimir force.

scholarly journals Radiative correction to the Casimir energy for massive scalar field on a spherical surface

2017 ◽  
Vol 32 (24) ◽  
pp. 1750128 ◽  
Author(s):  
M. A. Valuyan
Keyword(s):  
Scalar Field ◽  
Radiative Correction ◽  
Spherical Surface ◽  
Perturbation Expansion ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Massive Scalar ◽  
Massive Scalar Field ◽  
Free Theory

In this paper, the first-order radiative correction to the Casimir energy for a massive scalar field in the [Formula: see text] theory on a spherical surface with [Formula: see text] topology was calculated. In common methods for calculating the radiative correction to the Casimir energy, the counter-terms related to free theory are used. However, in this study, by using a systematic perturbation expansion, the obtained counter-terms in renormalization program were automatically position-dependent. We maintained that this dependency was permitted, reflecting the effects of the boundary conditions imposed or background space in the problem. Additionally, along with the renormalization program, a supplementary regularization technique that we named Box Subtraction Scheme (BSS) was performed. This scheme presents a useful method for the regularization of divergences, providing a situation that the infinities would be removed spontaneously without any ambiguity. Analysis of the necessary limits of the obtained results for the Casimir energy of the massive and massless scalar field confirmed the appropriate and reasonable consistency of the answers.

scholarly journals QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

1999 ◽  
Vol 11 (05) ◽  
pp. 519-532 ◽  
Author(s):  
SEBASTIANO CARPI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Scaling Limit ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Complex Scalar

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

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