Microscopic black hole and uncertainty principle with minimal length and momentum

TL;DR

This paper explores how a modified uncertainty principle with minimal length and momentum affects microscopic black hole thermodynamics, revealing a minimal temperature and phase transition similar to Schwarzschild-AdS black holes.

Contribution

It introduces a modified generalized uncertainty principle incorporating minimal length and momentum and analyzes its impact on black hole thermodynamics and phase transitions.

Findings

Minimal temperature for black holes due to momentum uncertainty

Existence of Hawking-Page phase transition

Altered black hole lifetime and emission rates

Abstract

We investigate a microscopic black hole in case of modified generalized uncertainty principle with a minimal uncertainty in position as well as in momentum. We calculate thermodynamical functions of a Schwarzschild black hole such as temperature, entropy and heat capacity. It is shown that incorporation of minimal uncertainty in momentum leads to minimal temperature of a black hole similarly as we have for Schwarzschschild-AdS black hole without minimal uncertainty. Minimal temperature gives rise to Hawking-Page phase transition. Emission rate equation and black hole lifetime are also obtained.