Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime

Giampiero Esposito; George M. Napolitano

doi:10.1088/0031-8949/90/7/074013

Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime

Giampiero Esposito^*, George M. Napolitano

^*Corresponding author for this work

Section of Environmental Health

Abstract

Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar Green functions for a Casimir-type apparatus in de Sitter spacetime. Working to first order in the small parameter of the problem, i.e. twice the gravity acceleration times the plates' separation divided by the speed of light in vacuum, suitable coordinates are considered for which the differential equations obeyed by the zeroth- and first-order Green functions can be solved in terms of special functions. This result can be used, in turn, to obtain, via the point-split method, the regularized and renormalized energy-momentum tensor both in the scalar case and in the physically more relevant electromagnetic case.

Original language	English
Article number	074013
Journal	Physica Scripta
Volume	90
Issue number	7
ISSN	0031-8949
DOIs	https://doi.org/10.1088/0031-8949/90/7/074013
Publication status	Published - 1 Jul 2015

Keywords

Casimir effect
Green function
Quantum gravity

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10.1088/0031-8949/90/7/074013

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abstract = "Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar Green functions for a Casimir-type apparatus in de Sitter spacetime. Working to first order in the small parameter of the problem, i.e. twice the gravity acceleration times the plates' separation divided by the speed of light in vacuum, suitable coordinates are considered for which the differential equations obeyed by the zeroth- and first-order Green functions can be solved in terms of special functions. This result can be used, in turn, to obtain, via the point-split method, the regularized and renormalized energy-momentum tensor both in the scalar case and in the physically more relevant electromagnetic case.",

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AU - Napolitano, George M.

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N2 - Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar Green functions for a Casimir-type apparatus in de Sitter spacetime. Working to first order in the small parameter of the problem, i.e. twice the gravity acceleration times the plates' separation divided by the speed of light in vacuum, suitable coordinates are considered for which the differential equations obeyed by the zeroth- and first-order Green functions can be solved in terms of special functions. This result can be used, in turn, to obtain, via the point-split method, the regularized and renormalized energy-momentum tensor both in the scalar case and in the physically more relevant electromagnetic case.

AB - Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar Green functions for a Casimir-type apparatus in de Sitter spacetime. Working to first order in the small parameter of the problem, i.e. twice the gravity acceleration times the plates' separation divided by the speed of light in vacuum, suitable coordinates are considered for which the differential equations obeyed by the zeroth- and first-order Green functions can be solved in terms of special functions. This result can be used, in turn, to obtain, via the point-split method, the regularized and renormalized energy-momentum tensor both in the scalar case and in the physically more relevant electromagnetic case.

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Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime

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