A generalized uncertainty-inspired quantum black hole

TL;DR

This paper derives a full spacetime metric for a quantum black hole inspired by uncertainty principles, addressing issues in previous models and showing the singularity is resolved with a regular, asymptotically flat spacetime.

Contribution

It introduces an improved scheme with momentum-dependent quantum parameters to extend the black hole metric, resolving classical singularities and ensuring regularity everywhere.

Findings

The resulting metric is asymptotically flat.

The Kretschmann scalar is finite everywhere.

Classical singularities are resolved in this model.

Abstract

We derive the full spacetime metric of a generalized uncertainty-inspired quantum black hole. We examine a previous model of the interior in this approach and show that extending its metric to the full spacetime leads to serious issues in the asymptotic region. To remedy this, we introduce an ``improved scheme'' mimicking a similar prescription used in loop quantum gravity, where the quantum parameters are made momentum-dependent. Under this scheme, we rework the interior of the black hole and extend it to the full spacetime. We find that the resulting metric is asymptotically flat and its associated Kretschmann scalar is regular everywhere. We also show that the null expansion and Raychaudhuri equation are regular everywhere in this spacetime, implying that the classical singularity is resolved.