Casimir effect due to a slowly rotating source in the weak field approximation

Abstract

We calculate the renormalized vacuum energy density for a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed very close to the surface of a rotating spherical gravitational source with mass $M$, radius $R$ and momentum angular $J$, at the equatorial region. We consider that the source rotates slowly and that the gravitational field is weak. Corrections to the Casimir energy density induced by the gravitational field generated by this source are calculated up to $M/R^2$ order. The obtained results show us that there is an important modification in the Casimir energy only in this order of approximation, which depends on the surface gravity as well as on the rotation of the source. Thermal corrections to the Casimir energy found also are calculated in all these orders.

15 pages. To appear in Physical Review D

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• Null Second Order Corrections to Casimir Energy in Weak Gravitational Field
• Thermal Casimir Effect in Kerr Space-time
• Theoretical analysis of Casimir and thermal Casimir effect in stationary space-time
• Null second order corrections to Casimir energy in weak gravitational field: The Schwinger's approach
• Dependence of the Black-body Force on Spacetime Geometry and Topology
• Quasi-local stress-tensor formalism and the Casimir effect
• Casimir effect in conformally flat spacetimes