Finite temperature Casimir effect for a spinor field in cosmic dispiration spacetime

TL;DR

This paper investigates the finite temperature Casimir effect for a massive spinor field in cosmic dispiration spacetime, revealing how topology, boundary conditions, and temperature influence the Casimir energy and its corrections.

Contribution

It extends the analysis of the Casimir effect to cosmic dispiration spacetime, incorporating finite temperature effects and generalized boundary conditions with detailed heat kernel coefficient analysis.

Findings

Casimir energy depends on topology and boundary conditions.

Renormalized energy can be positive or negative, decreasing with mass.

High-temperature free energy vanishes, low-temperature energy dominates.

Abstract

This study explores the finite temperature Casimir effect for a massive spinor field in cosmic dispiration spacetime, formed by the combination of a cosmic string and a screw dislocation using the generalized zeta function regularization method. First, we examine the cosmic string spacetime with a quasi-antiperiodic boundary condition, where the Casimir energy and its corrections depend on two nonzero heat kernel coefficients, one associated with the Euclidean divergence and the other with the nontrivial topology, both vanishing when renormalized. Interestingly, for specific choice of parameters the quasi-antiperiodicity effect can entirely cancel out the topological contribution, leaving only the Euclidean divergence. We then extend this analysis to cosmic dispiration spacetime. This configuration alters the spacetime topology, modifying the structure of the heat kernel coefficient related to the new nontrivial topology. In this case, the renormalized Casimir energy density can take positive or negative values and decreases exponentially as the field mass increases. Additionally, we examine the asymptotic behavior of the renormalized temperature correction term in the massless regime, showing that the spinor vacuum free energy vanishes at very high temperatures. At very low temperatures, it is dominated by the zero-temperature Casimir energy density.