Rainbow's Gravity Corrections to the Black Hole Global Casimir Effect

TL;DR

This paper investigates how Rainbow's Gravity modifies the global Casimir effect around mini black holes near the Planck scale, revealing singularities and universal properties of the remnant Casimir tension.

Contribution

It provides the first analysis of Rainbow's Gravity corrections to the global Casimir effect in black hole backgrounds, including finite temperature effects and the behavior near zero mass.

Findings

Singular behavior at specific parameter limits

Remnant Casimir tension remains finite and unaffected by Rainbow's Gravity

Universal properties of the Casimir tension in the zero-mass limit

Abstract

In this manuscript we compute corrections to the global Casimir effect at zero and finite temperature due to Rainbow's Gravity (parametrized by $\xi$). For this we use the solutions for the scalar field with mass $m$ in the deformed Schwarzschild background and the corresponding quantized energies of the system, which represent the stationary states of the field and yield the stable part of the quantum vacuum energy. The analysis is made here by considering the limit for which the source mass, $M$, approaches zero, in order to verify the effects on the global Casimir effect in mini black holes near to the Planck scale, $\omega_P$. We find a singular behavior for the regularized vacuum energy at zero temperature and for all the corresponding thermodynamic quantities when $m^2=\omega^2_P/\xi$, what can be seen as the limit of validity of the model. Furthermore, we show that the remnant Casimir tension over the event horizon in the limit $M\to 0$ is finite for any temperature and all the space of parameters. In fact we show that the remnant tension receives no corrections from Rainbow's Gravity. This points to the fact that such a behavior may be an universal property of this kind of system.