Recent work in the literature had evaluated the energy-momentum tensor of a Casimir apparatus in a weak gravitational field, for an electromagnetic field subject to perfect conductor boundary conditions on parallel plates. The Casimir apparatus was then predicted to experience a tiny push in the upward direction, and the regularized energy-momentum tensor was evaluated to first order in the gravitational acceleration. This analysis made it desirable to assess what happens in a simpler case. For this purpose, the present paper studies a free, real massless scalar field subject to homogeneous Dirichlet conditions on the parallel plates. Working again to first order in the constant gravity acceleration, the resulting regularized and renormalized energy-momentum tensor is found to be covariantly conserved, while the trace anomaly vanishes if the massless scalar field is conformally coupled to gravity. Conformal coupling also ensures a finite Casimir energy and finite values of the pressure upon parallel plates.
Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: Scalar case / Esposito, G.; Napolitano, G.; Rosa, Luigi. - In: PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY. - ISSN 1550-7998. - STAMPA. - 77:10(2008), pp. 105011-1-105011-7. [10.1103/PhysRevD.77.105011]
Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: Scalar case
G. EspositoPrimo
;ROSA, LUIGIUltimo
2008
Abstract
Recent work in the literature had evaluated the energy-momentum tensor of a Casimir apparatus in a weak gravitational field, for an electromagnetic field subject to perfect conductor boundary conditions on parallel plates. The Casimir apparatus was then predicted to experience a tiny push in the upward direction, and the regularized energy-momentum tensor was evaluated to first order in the gravitational acceleration. This analysis made it desirable to assess what happens in a simpler case. For this purpose, the present paper studies a free, real massless scalar field subject to homogeneous Dirichlet conditions on the parallel plates. Working again to first order in the constant gravity acceleration, the resulting regularized and renormalized energy-momentum tensor is found to be covariantly conserved, while the trace anomaly vanishes if the massless scalar field is conformally coupled to gravity. Conformal coupling also ensures a finite Casimir energy and finite values of the pressure upon parallel plates.File | Dimensione | Formato | |
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