Quantum Extension of the Kruskal Space-time

TL;DR

This paper presents a quantum-corrected extension of Kruskal black hole spacetime using loop quantum gravity, resolving singularities and revealing a rich structure of multiple regions with bounded curvature.

Contribution

It introduces a novel quantum extension of Kruskal spacetime incorporating loop quantum gravity effects, with features like singularity resolution and bounded curvature scalars.

Findings

Singularities are resolved by quantum geometry effects.

The extended spacetime admits multiple trapped and asymptotic regions.

Curvature scalars have uniform, mass-independent upper bounds.

Abstract

A new description of macroscopic Kruskal black holes that incorporates the quantum geometry corrections of loop quantum gravity is presented. It encompasses both the `interior' region that contains classical singularities and the `exterior' asymptotic region. Singularities are naturally resolved by the quantum geometry effects of loop quantum gravity. The resulting quantum extension of space-time has the following features: (i) It admits an infinite number of trapped, anti-trapped and asymptotic regions; (ii) All curvature scalars have uniform (i.e., mass independent) upper bounds; (iii) In the large mass limit, all asymptotic regions of the extension have the same ADM mass; (iv) In the low curvature region (e.g., near horizons) quantum effects are negligible, as one would physically expect; and (v) Final results are insensitive to the fiducial structures that have to be introduced to construct the classical phase space description (as they must be). Previous effective theories [1-10] shared some but not all of these features. We compare and contrast our results with those of these effective theories and also with expectations based on the AdS/CFT conjecture [11]. We conclude with a discussion of limitations of our framework, especially for the analysis of evaporating black holes.