The effects of a minimal length on the Kerr metric and the Hawking temperature

TL;DR

This paper investigates how introducing a minimal length in the pseudo complex General Relativity framework affects the Kerr metric and Hawking temperature, revealing significant effects for small black holes relevant to early universe conditions.

Contribution

It extends the analysis of Hawking temperature and entropy to the pcGR framework with a minimal length, highlighting effects on small black holes and dark energy implications.

Findings

Minimal length influences Hawking temperature for small black holes.

Dark energy distribution impacts black hole thermodynamics.

Negative temperatures may appear in certain regimes.

Abstract

A brief review of the pseudo complex General Relativity (pcGR) will be presented, with its consequences, as the accumulation of a dark energy around a mass and a generalized Machs principle. The main objective in this contribution is to determine the Hawking temperature and the Entropy for various limits: i) The pc-Schwarzschild case with no minimal length present, ii) the pc-Kerr metric without a minimal length and iii) the general case, the pc-Kerr metric with a minimal length present. The physical consequences of a minimal length will be discussed, a possible interpretation of a gravitational Schwinger effect and the appearance of negative temperature. For large masses a minimal length does not show any sensible effect, but only for very small masses, several orders of the Planck mass, where non-trivial effects emerge, important for the production of mini-black holes in the early universe. Our results are more general than being restricted to pcGR. Any other model which assumes a distribution of dark energy around a stellar body produces the same effects. In contrast to these models, pcGR demands the presence of a dark energy term.