Thermal Casimir effect in G\"{o}del-type universes

TL;DR

This paper investigates the thermal Casimir effect for a scalar field in G"{o}del-type universes using Thermo Field Dynamics, revealing temperature-dependent transitions from attractive to repulsive Casimir forces.

Contribution

It introduces a novel analysis of the thermal Casimir effect in G"{o}del-type spacetimes using Thermo Field Dynamics, highlighting temperature-induced force behavior.

Findings

Casimir effect is attractive at zero temperature in G"{o}del-type universes.

Finite temperature can induce a transition to a repulsive Casimir force.

The approach unifies topological and thermal effects in curved spacetime.

Abstract

In this paper, a massless scalar field coupled to gravity is considered. Then the Casimir effect at finite temperature is calculated. Such development is carried out in the Thermo Field Dynamics formalism. This approach presents a topological structure that allows for investigating the effects of temperature and the size effect in a similar way. These effects are calculated considering G\"{o}del-type solutions as a gravitational background. The Stefan-Boltzmann law and its consistency are analyzed for both causal and non-causal G\"{o}del-type regions. In this space-time and for any region, the Casimir effect at zero temperature is always attractive. However, at finite temperature, a repulsive Casimir effect can emerge from a critical temperature.