Quantum Dynamics of the Schwarzschild Interior in Ashtekar-Barbero Variables with Minimal Length Effects

TL;DR

This paper investigates how minimal-length effects, introduced via a generalized uncertainty principle, influence the quantum dynamics of the Schwarzschild black hole interior, potentially resolving classical singularities.

Contribution

It demonstrates that minimal-length effects modify the quantum interior dynamics, suppressing the annihilation-to-nothing scenario and challenging its role in singularity resolution.

Findings

GUP induces minimal-length effects in the Wheeler-DeWitt equation.

Minimal-length effects suppress the annihilation-to-nothing behavior.

Quantum dynamics are qualitatively altered by GUP corrections.

Abstract

We study the quantum dynamics of the Schwarzschild interior in the Ashtekar-Barbero formulation, focusing on the fate of the classical singularity and the annihilation-to-nothing scenario. Using minisuperspace Wheeler-DeWitt quantization, we first analyze the standard Schr\"odinger representation and show that the annihilation-to-nothing behavior appears only for a specific choice of factor ordering and is not generic. We then introduce a generalized uncertainty principle (GUP), which induces minimal-length effects through a deformation of the canonical algebra. Solving the modified Wheeler-DeWitt equation and constructing Gaussian wave packets localized at the horizon, we find that the annihilation-to-nothing behavior is suppressed once the GUP corrections are included. Our results indicate that minimal-length effects qualitatively alter the quantum interior dynamics and challenge the robustness of this scenario as a mechanism for singularity resolution.