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

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.