Probing the interior of the Schwarzschild black hole using congruences: LQG vs. GUP

TL;DR

This paper compares how loop quantum gravity and generalized uncertainty principle approaches describe the interior structure and singularity of Schwarzschild black holes, using congruences and the Raychaudhuri equation, reaffirming finiteness of key scalars in certain models.

Contribution

It provides new results on the behavior of spacetime and singularities in black holes within LQG and GUP frameworks, highlighting differences based on algebra modifications.

Findings

In LQG, the expansion scalar and Kretschmann scalar are finite inside the black hole.

Two GUP models with configuration-variable modifications also yield finite scalars.

The algebraic structure influences the singularity resolution in these models.

Abstract

We review, as well as provide some new results regarding the study of the structure of spacetime and the singularity in the interior of the Schwarzschild black hole in both loop quantum gravity and generalized uncertainty principle approaches, using congruences and their associated expansion scalar and the Raychaudhuri equation. We reaffirm previous results that in loop quantum gravity, in all three major schemes of polymer quantization, the expansion scalar, Raychaudhuri equation and the Kretschmann scalar remain finite everywhere in the interior. In the context of the eneralized uncertainty principle, we show that only two of the four models we study lead to similar results. These two models have the property that their algebra is modified by configuration variables rather than the momenta.