Geometry of a generalized uncertainty-inspired spacetime

TL;DR

This paper explores a generalized uncertainty-inspired quantum black hole geometry, revealing a non-symmetric metric, a null surface at r=0, a repulsive core, and a non-traversable wormhole solution, suggesting a possible black hole remnant.

Contribution

It introduces a novel black hole model with a non-symmetric metric and analyzes its geometric and physical properties, including singularity resolution and wormhole features.

Findings

r=0 is a null surface, not a transition or bounce

The interior null geodesic expansion vanishes at r=0

The spacetime violates energy conditions, indicating a repulsive core

Abstract

We examine the geometry of a generalized uncertainty-inspired quantum black hole. The diagonal line element is not $t$-$r$ symmetric, i.e. $g_{00} \ne -1/g_{11}$, which leads to an interesting approach to resolving the classical curvature singularity. In this paper, we show, in Schwarzschild coordinates, the $r = 0$ coordinate location is a null surface which is not a transition surface or leads to a black bounce. We find the expansion of null geodesic congruences in the interior turn around then vanishes at $r = 0$, and the energy conditions are predominately violated indicating a repulsive gravitational core. In addition, we show that the line element admits a wormhole solution which is not traversable, and the black hole at its vanishing horizon radius could be interpreted as a remnant.