Deformed algebra and the effective dynamics of the interior of black holes

TL;DR

This paper introduces a deformation of the classical Hamiltonian for black hole interiors inspired by generalized uncertainty principles, leading to singularity resolution and a minimum radius within the black hole.

Contribution

It proposes a novel deformation of the canonical algebra in black hole interior models, resulting in effective dynamics that resolve singularities.

Findings

Singularity is resolved with the deformation

A minimum nonzero radius for infalling spheres is established

Deformation parameters influence the black hole interior structure

Abstract

We consider the classical Hamiltonian of the interior of the Schwarzschild black hole in Ashtekar-Barbero connection formalism. Then, inspired by generalized uncertainty principle models, we deform the classical canonical algebra and derive the effective dynamics of the model under this modification. We show that such a deformation leads to the resolution of the singularity of the black hole and a minimum nonzero radius for the infalling 2-spheres, provided that the deformation parameters are chosen to be negative.