Thermal Casimir Effect in Kerr Space-time

TL;DR

This paper analyzes the thermal Casimir effect for a scalar field between moving plates in Kerr space-time, deriving analytical expressions for free energy and internal energy, and exploring their low-temperature behavior.

Contribution

It provides the first analytical derivation of the thermal Casimir effect in Kerr space-time with moving plates, including temperature and geometry dependencies.

Findings

Thermal correction to Casimir energy depends on proper temperature and geometry.

Analytical expressions for renormalized free energy and internal energy are obtained.

Low-temperature asymptotic behavior of Casimir quantities is characterized.

Abstract

We investigate the thermal Casimir effect of a massless scalar field for two parallel plates moving in the equatorial orbit in Kerr space-time. Under the assumption that the typical cavity size is much smaller than the orbital radius, proposed by Sorge, we deduce the analytical expression of the renormalized free energy in this curved space-time. We also get the analytical representation for the renormalized internal energy, and find that there is a thermal correction to the Casimir energy, which depends on the proper temperature and the proper geometrical parameters of the plates. The asymptotic behavior of the Casimir free energy, entropy and internal energy at low temperature is also investigated.