Avoidance of singularities in asymptotically safe Quantum Einstein Gravity

TL;DR

This paper derives new spherically symmetric solutions in asymptotically safe Quantum Einstein Gravity, showing how quantum effects can resolve singularities near black hole centers by modifying spacetime structure.

Contribution

It introduces novel solutions that incorporate a scale-dependent cosmological constant, demonstrating potential singularity avoidance in quantum gravity models.

Findings

One solution is timelike geodesically complete with a repulsive core.

Another family of solutions has finite curvature invariants at a minimum radius.

Solutions suggest quantum effects can prevent classical singularities.

Abstract

New general spherically symmetric solutions have been derived with a cosmological "constant" \Lambda as a source. This \Lambda field is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.