Energy-momentum tensor for a Casimir apparatus in a weak gravitational field

Abstract

The influence of the gravity acceleration on the regularized energy-momentum tensor of the quantized electromagnetic field between two plane parallel conducting plates is derived. We use Fermi coordinates and work to first order in the constant acceleration parameter. A perturbative expansion, to this order, of the Green functions involved and of the energy-momentum tensor is derived by means of the covariant geodesic point splitting procedure. In correspondence to the Green functions satisfying mixed and gauge-invariant boundary conditions, and Ward identities, the energy-momentum tensor is covariantly conserved and satisfies the expected relation between gauge-breaking and ghost parts. A more systematic derivation is therefore obtained of the theoretical prediction according to which the Casimir device in a weak gravitational field will experience a tiny push in the upwards direction.

Equations (4.4), (5.1), (5.2), (5.4), (B9) have been amended, while equations (5.7) and (5.8) have been deleted. Comments have been amended accordingly

Cited by in corpus (38)

• How Does Casimir Energy Fall?
• Relativistic mechanics of Casimir apparatuses in a weak gravitational field
• Recent Developments in the Casimir Effect
• How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy
• Towards weighing the condensation energy to ascertain the Archimedes force of vacuum
• How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy
• Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: scalar case
• From Rindler space to the electromagnetic energy-momentum tensor of a Casimir apparatus in a weak gravitational field
• Vacuum energy and the spacetime index of refraction: A new synthesis
• Gravitational and Inertial Mass of Casimir Energy
• General Transformation Formulas for Fermi-Walker Coordinates
• Fermi coordinates, simultaneity, and expanding space in Robertson-Walker cosmologies
• Quantum Electromagnetic Stress Tensor in an Inhomogeneous Medium
• Casimir effect of two conducting parallel plates in a general weak gravitational field
• Exact Fermi coordinates for a class of spacetimes
• Electromagnetic Casimir effect and the spacetime index of refraction
• Casimir effect in a weak gravitational field and the spacetime index of refraction
• Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
• The Archimedes experiment
• Energy-momentum tensor for a scalar Casimir apparatus in a weak gravitational field: Neumann conditions
• Quasi-local Casimir energy and vacuum buoyancy in a weak gravitational field
• Whether an enormously large energy density of the quantum vacuum is catastrophic
• Pre-big bang geometric extensions of inflationary cosmologies
• Centenary of Alexander Friedmann's Prediction of the Universe Expansion and the Quantum Vacuum
• How Does Quantum Vacuum Energy Accelerate?
• Maximal Fermi charts and geometry of inflationary universes
• Vacuum fluctuation force on a rigid Casimir cavity in de Sitter and Schwarzschild-de Sitter spacetime
• Vacuum energy, the Casimir effect, and Newton's non-constant
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Archimedes Force on Casimir Apparatus
• The gravity of magnetic stresses and energy
• An extension of Poincaré group based on generalized Fermi-Walker coordinates
• Quantum vacuum under mixed boundary conditions: the case for curved spacetime
• Quasi-local stress-tensor formalism and the Casimir effect
• Some remarks on axion dark matter, dark energy and energy of the quantum vacuum
• Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime
• Novel features of the energy momentum tensor of a Casimir apparatus in a weak gravitational field
• Fermionic Casimir densities for a uniformly accelerating mirror in the Fulling-Rindler vacuum