Rainbow’s gravity corrections to the black hole global Casimir effect

In this manuscript, we compute corrections to the global Casimir effect at zero and finite temperature due to rainbow 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, 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 $$M\rightarrow 0$$ is finite for any temperature and all the space of parameters. In fact, we show that the remnant tension receives no corrections from rainbow gravity. This points to the fact that such a behavior may be an universal property of this kind of system.