Energy-momentum tensor for a scalar Casimir apparatus in a weak gravitational field: Neumann conditions

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We consider a Casimir apparatus consisting of two perfectly conducting parallel plates, subject to the weak gravitational field of the Earth. The aim of this paper is the calculation of the energy-momentum tensor of this system for a free, real massless scalar field satisfying Neumann boundary conditions on the plates. The small gravity acceleration (considered here as not varying between the two plates) allows us to perform all calculations to first order in this parameter. Some interesting results are found: a correction, depending on the gravity acceleration, to the well-known Casimir energy and pressure on the plates. Moreover, this scheme predicts a tiny force in the upwards direction acting on the apparatus. These results are supported by two consistency checks: the covariant conservation of the energy-momentum tensor and the vanishing of its regularized trace, when the scalar field is conformally coupled to gravity.


  • Giampiero Esposito
  • George Napolitano
  • Luigi Rosa
External organisations
  • External Organization - Unknown
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics
Original languageEnglish
Pages (from-to)107701-1-107701-4
JournalPhysical Review D (Particles, Fields, Gravitation and Cosmology)
Issue number10
Publication statusPublished - 2008
Publication categoryResearch
Externally publishedYes