Casimir Effect in the Kerr Spacetime with Quintessence

TL;DR

This paper investigates how the Casimir energy of a scalar field is affected by the gravitational field of a rotating black hole surrounded by quintessence, revealing parameter dependencies and potential experimental constraints.

Contribution

It provides a detailed analysis of the Casimir effect in Kerr spacetime with quintessence, including parameter dependencies and observational constraints.

Findings

Casimir energy depends on source mass, angular momentum, and quintessence parameters.

At the north pole, Casimir energy is unaffected by quintessence.

Constraints on quintessence parameters are derived from current measurement uncertainties.

Abstract

We calculate the Casimir energy of a massless scalar field in a cavity formed by nearby parallel plates orbiting a rotating spherical body surrounded by quintessence, investigating the influence of the gravitational field on that energy, at zero temperature. This influence includes the effects due to the spacetime dragging caused by the source rotation as well as those ones due to the quintessence. We show that the energy depends on all the involved parameters, as source mass, angular momentum and quintessence state parameter, for any radial coordinate and polar angle. We show that at the north pole the Casimir energy is not influenced by the quintessential matter. At the equatorial plane, when the quintessence is canceled, the result obtained in the literature is recovered. Finally, constraints in the quintessence parameters are obtained from the uncertainty in the current measurements of Casimir effect.