The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length

TL;DR

This paper extends the uncertainty principle to include a minimal length in (A)dS space and analyzes its effects on Hawking temperature, showing it generally increases the temperature and influences black hole phase transitions.

Contribution

It introduces a generalized uncertainty principle with a minimal length in (A)dS space and studies its impact on Hawking radiation and black hole phase transitions.

Findings

Generalized uncertainty principle increases Hawking temperature.

Minimal length leads to faster black hole decay.

Revisits black hole-string phase transition under GUP.

Abstract

Recently, the Heisenberg's uncertainty principle has been extended to incorporate the existence of a large (cut-off) length scale in de Sitter or anti-de Sitter space, and the Hawking temperatures of the Schwarzshild-(anti) de Sitter black holes have been reproduced by using the extended uncertainty principle. I generalize the extended uncertainty to the case with an absolute minimum length and compute its modification to the Hawking temperature. I obtain a general trend that the generalized uncertainty principle due to the absolute minimum length ``always'' increases the Hawking temperature, implying ``faster'' decay, which is in conformity with the result in the asymptotically flat space. I also revisit the ``black hole-string'' phase transition, in the context of the generalized uncertainty principle.