The pseudo‐complex General Relativity and effects of a minimal length on the structure of black holes

Abstract

After resuming some main predictions of the pseudo‐complex General Relativity (pcGR), the effects of a minimal length, on the structure near the event horizon of a Schwarzschild and Kerr black hole, are investigated within the pcGR. It is shown that for small mass black holes there are strong effects, for example, avoiding the accumulation of mass, which might be important in the formation of primordial black holes during the Big Bang. The pcGR adds to the metric a contribution characterized by a parameter α$$ \alpha $$, which has a critical value at which barely an event horizon exists. For macroscopic black holes, these effects vanished for below and above this critical value, but at the critical value effects still persist up to m=10−13$$ m={10}^{-13} $$ cm, though quickly disappearing. For very large mass black holes the minimal length can be safely neglected. The limit between a small and a macroscopic black hole, in units of length, is between 10−15$$ {10}^{-15} $$ cm and 10−13$$ {10}^{-13} $$ cm.