Effective dynamics of the Schwarzschild black hole interior with inverse triad corrections

TL;DR

This paper investigates the effects of inverse triad quantum corrections on the Schwarzschild black hole interior within loop quantum gravity, showing that such corrections modify key features like the bounce radius and white hole mass.

Contribution

It introduces two prescriptions for implementing inverse triad corrections that address rescaling issues, extending previous models to include quantum effects.

Findings

Singularity resolution remains valid with quantum corrections.

The minimum radius at bounce and white hole mass are affected by inverse triad corrections.

Rescaling prescriptions influence physical results under noncompact topology.

Abstract

We reconsider the study of the interior of the Schwarzschild black hole now including inverse triad quantum corrections within loop quantization. We derive these corrections and show that they are are related to two parameters $\delta_b, \delta_c$ associated to the minimum length in the radial and angular directions, that enter Thiemann's trick for quantum inverse triads. Introduction of such corrections may lead to non-invariance of physical results under rescaling of the fiducial volume needed to compute the dynamics, due to noncompact topology of the model. So, we put forward two prescriptions to resolve this issue. These prescriptions amount to interchange $\delta_b, \delta_c$ in classical computations in Thiemann's trick. By implementing the inverse triad corrections we found, previous results such as singularity resolution and black-to-white hole bounce hold with different values for the minimum radius-at-bounce, and the mass of the white hole.