The final stage of gravitationally collapsed thick matter layers

TL;DR

This paper explores the final state of gravitational collapse of thick matter layers, proposing regular, singularity-free solutions inspired by non-commutative geometry, with implications for black hole physics and Hawking radiation.

Contribution

It introduces new Einstein's equation solutions for thick shells that are regular and interpolate between Minkowski and Schwarzschild geometries, extending black hole models with minimal length effects.

Findings

Solutions are curvature singularity free.

Black hole solutions exist only for shells with mass above a critical value.

Modified Hawking temperature and Area Law are derived.

Abstract

In the presence of a minimal length physical objects cannot collapse to an infinite density, singular, matter point. In this note we consider the possible final stage of the gravitational collapse of "thick" matter layers. The energy momentum tensor we choose to model these shell-like objects is a proper modification of the source for "non-commutative geometry inspired", regular black holes. By using higher momenta of Gaussian distribution to localize matter at finite distance from the origin, we obtain new solutions of the Einstein's equation which smoothly interpolates between Minkowski geometry near the center of the shell and Schwarzschild spacetime far away from the matter layer. The metric is curvature singularity free. Black hole type solutions exist only for "heavy" shells, i.e. $M\ge M_{e}$, where $M_{e}$ is the mass of the extremal configuration. We determine the Hawking temperature and a modified Area Law taking into account the extended nature of the source.