Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: Scalar case.
Esposito, Giampiero; Napolitano, George; Rosa, Luigi (2008). Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: Scalar case.. Physical Review D (Particles, Fields, Gravitation and Cosmology), 77,, 1 - 105011
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Published
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English
Authors:
Esposito, Giampiero
;
Napolitano, George
;
Rosa, Luigi
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.
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