Relativistic mechanics of Casimir apparatuses in a weak gravitational field

Abstract

This paper derives a set of general relativistic Cardinal Equations for the equilibrium of an extended body in a uniform gravitational field. These equations are essential for a proper understanding of the mechanics of suspended relativistic systems. As an example, the prototypical case of a suspended vessel filled with radiation is discussed. The mechanics of Casimir apparatuses at rest in the gravitational field of the Earth is then considered. Starting from an expression for the Casimir energy-momentum tensor in a weak gravitational field recently derived by the authors, it is here shown that, in the case of a rigid cavity supported by a stiff mount, the weight of the Casimir energy $E_C$ stored in the cavity corresponds to a gravitational mass $M=E_C/c^2$, in agreement with the covariant conservation law of the regularized energy-momentum tensor. The case of a cavity consisting of two disconnected plates supported by separate mounts, where the two measured forces cannot be obtained by straightforward arguments, is also discussed.

9 pages, improved presentation and new references added

Cited by in corpus (15)

• How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy
• Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: scalar case
• Gravitational and Inertial Mass of Casimir Energy
• Rotating Casimir systems: magnetic-field-enhanced perpetual motion, possible realization in doped nanotubes, and laws of thermodynamics
• Thermal Casimir Effect in Kerr Space-time
• Energy-momentum tensor for a scalar Casimir apparatus in a weak gravitational field: Neumann conditions
• Whether an enormously large energy density of the quantum vacuum is catastrophic
• Quasi-local Casimir energy and vacuum buoyancy in a weak gravitational field
• Centenary of Alexander Friedmann's Prediction of the Universe Expansion and the Quantum Vacuum
• On a possible method of Casimir pressure renormalization in a ball
• Vacuum energy, the Casimir effect, and Newton's non-constant
• Vacuum fluctuation force on a rigid Casimir cavity in de Sitter and Schwarzschild-de Sitter spacetime
• The gravity of magnetic stresses and energy
• Quasi-local stress-tensor formalism and the Casimir effect
• Novel features of the energy momentum tensor of a Casimir apparatus in a weak gravitational field