Non-Singular Gravitational Collapse through Modified Heisenberg Algebra

TL;DR

This paper demonstrates that incorporating a modified algebra inspired by quantum gravity effects can prevent singularities in gravitational collapse, leading to stable, non-singular, asymptotically static configurations in both Newtonian and relativistic models.

Contribution

It introduces a modified algebra approach to gravitational collapse, showing the removal of singularities and stability of non-singular configurations in classical models.

Findings

Collapse is stabilized to an asymptotically static state above the horizon.

Singularity is removed in both Newtonian and relativistic models.

Non-singular configurations are stable under certain perturbations.

Abstract

We study the effects of cut-off physics, in the form of a modified algebra inspired by Polymer Quantum Mechanics and by the Generalized Uncertainty Principle representation, on the collapse of a spherical dust cloud. We analyze both the Newtonian formulation, originally developed by Hunter, and the general relativistic formulation, that is the Oppenheimer-Snyder model; in both frameworks we find that the collapse is stabilized to an asymptotically static state above the horizon, and the singularity is removed. In the Newtonian case, by requiring the Newtonian approximation to be valid, we find lower bounds of the order of unity (in Planck units) for the deformation parameter of the modified algebra. We then study the behaviour of small perturbations on the non-singular collapsing backgrounds, and find that for certain range of the parameters (the polytropic index for the Newtonian case and the sound velocity in the relativistic setting) the collapse is stable to perturbations of all scales, and the non-singular super-Schwarzschild configurations have physical meaning.