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

Abstract

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 energymomentum tensor of this system for a free, real massless scalar field satisfying Neumann boundary conditions on the plates. The small gravity acceleration (here considered 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.

Casimir effect of two conducting parallel plates in a general weak gravitational field

“…The above energy densities are exactly the results (5.2) in [15][16][17][18][19], (3.4) in [22], and (5.4) in [21].…”

“…In fact, some non-trivial topologies in curved spacetime do the same job as a boundary does [6,7]. The Casimir energy in curved spacetime has also been analyzed by many authors ( [1,2,6,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and references therein). Recently, a Casimir apparatus consisting of two ideal conducting parallel plates in the weak field limit of the Kerr and the Horava-Lifshitz spacetimes has been studied in [8][9][10][11].…”

Whether an Enormously Large Energy Density of the Quantum Vacuum Is Catastrophic

“…It is important to underline, however, that the finite Casimir energy density and force acting between the boundary surfaces are obtained after subtracting a divergent energy density of the quantum vacuum in an unrestricted space, i.e., disregarding the same quantity as in standard quantum field theory. It cannot be too highly stressed that only this finite and measurable energy density is a source of gravitational interaction [11][12][13]. The Casimir-like energy density also arises in spaces with nontrivial topology due to identification conditions imposed on the quantized fields [14][15][16].…”

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

“…A simpler check is also available, i.e., the evaluation of T µν for a scalar type Casimir apparatus, for which Dirichlet or Neumann boundary conditions on the plates are imposed [5,6], rather than the mixed boundary conditions appropriate for gauge fields [15,16].…”

“…As we said before, in [4][5][6], such techniques have been used to establish on firm ground the physical prediction [7] that a Casimir apparatus, when put in a weak gravitational field, will experience a very tiny push in the upwards direction, behaving therefore as if it were equivalent to an experimental device of negative mass. Although the resulting force is so small that only a significant progress in signal-modulation techniques would make it testable [7], the effect is, conceptually, of extreme interest, and physicists should have learned, by now, how important can gedanken experiments turn out to be.…”