Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-03-07
Phys.Rev.D76:025008,2007
Physics
High Energy Physics
High Energy Physics - Theory
9 pages, improved presentation and new references added
Scientific paper
10.1103/PhysRevD.76.025008
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.
Bimonte Giuseppe
Calloni Enrico
Esposito Giampiero
Rosa Luigi
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