Black hole thermodynamics in the presence of a maximal length and minimum measurable in momentum

TL;DR

This paper explores how minimal measurable momentum and maximal length modify black hole thermodynamics, revealing minimum temperature, maximum mass, and stability conditions, along with impacts on the Unruh effect.

Contribution

It introduces a novel framework incorporating minimal momentum and maximal length into black hole thermodynamics, deriving new temperature, entropy, and stability conditions.

Findings

Black hole temperature has a minimum value $T_{min}$.

Black hole mass has a maximum value $M_{max}$.

Black holes are stable within a specific mass range.

Abstract

In this work, incorporating the effect of the minimum measurable in momentum and maximal length, we studied thermodynamics property of Schwarzschild black hole and the Unruh effect. {\color{red} According to this scenario, we see that the black hole temperature cannot be smaller than a certain minimum value of $ T_{\min} $. Moreover, we find that black hole mass cannot be larger than a maximum mass value of $M_{\max }$. Considering these findings first we compute the corrected Hawking temperature versus the mass and examine its characteristic behavior. Then, we derive the black hole's entropy and heat capacity. We find that the black hole is stable when $\frac{M_{\max }}{\sqrt{3}}<M<M_{\max }$. Finally, we examined the modified Unruh effect. We find that the modified Unruh temperature explicitly depends on $\alpha$.