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arXiv · 0803.0861

Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: scalar case

Giampiero Esposito·George M. Napolitano·Luigi Rosa
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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 upwards direction, and the regularized energy-momentum tensor was found to have a trace anomaly. The latter, unexpected property made it compelling 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 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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Giampiero Esposito, George M. Napolitano, Luigi Rosa. 2008-03-06. Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: scalar case. https://doi.org/10.1103/physrevd.77.105011

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