Effective spherical symmetry in Loop Quantum Gravity: A path integral approach

TL;DR

This paper develops a loop quantum gravity model for spherically symmetric vacuum space-times using a path integral approach, revealing quantum corrections that modify classical black hole solutions and potentially resolve singularities.

Contribution

It introduces a novel path integral method to derive effective loop quantum corrections for spherically symmetric space-times, including inverse triad and holonomy effects.

Findings

Quantum corrections modify the classical Hamiltonian constraint.

Effective geometry describes black holes without singularities.

Preliminary evidence suggests holonomy corrections may resolve singularities.

Abstract

In this work a loop quantum corrected model is obtained for spherically symmetric space-times in the vacuum. This effective model is derived by the use of the path integral method, previously employed in several models of Loop Quantum Cosmology. Our principal aim is to find explicit corrections corresponding to inverse triad and holonomy effects that commonly arise from the loop quantization procedure. These corrections modify the Hamiltonian constraint of the classical theory, adding quantum parameters that represent the length of the holonomies considered during quantization. The semiclassical theory yielded reduces to the classical case when small values of such length are taken to be small. Solutions to the effective dynamics of a simplified version of the complete corrected theory are then found and used to describe an effective geometry with inverse triad corrections. This modified space-time represents a black hole with a curvature singularity in its interior which, contrary to its classical counterpart, does not lead to null geodesic incompleteness. For the case of holonomy corrections, preliminary arguments are given in favor of a potential singularity resolution.