Theoretical analysis of Casimir and thermal Casimir effect in stationary space-time

TL;DR

This paper provides a theoretical analysis of the Casimir and thermal Casimir effects in stationary curved space-time, highlighting how these quantum phenomena are affected by gravitational fields and space-time geometry.

Contribution

It introduces a scheme to renormalize thermal corrections to the Casimir effect in curved space-time and explores the influence of metric components on Casimir energy and thermodynamics.

Findings

Casimir energy depends on the 00-component of the metric.

Thermal corrections depend on proper temperature, geometry, and metric determinant.

The scheme for renormalizing thermal corrections is proposed.

Abstract

We investigate Casimir effect as well as thermal Casimir effect for a pair of parallel perfectly plates placed in general stationary space-time background. It is found that the Casimir energy is influenced by the 00-component of metric and the corresponding quantity in dragging frame. We give a scheme to renormalize thermal correction to free energy in curved space-time. It is shown that the thermal corrections to Casimir thermodynamic quantities not only depend on the proper temperature and proper geometrical parameters of the plates, but also on the determinant of space-time metric.