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

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.