Gravitational Collapse of the Shells with the Smeared Gravitational Source in Noncommutative Geometry

TL;DR

This paper investigates the gravitational collapse of shells with generalized matter in noncommutative geometry, showing conditions under which black holes or naked singular shells form, and exploring the effects of noncommutative corrections.

Contribution

It introduces a model of shell collapse with smeared sources in noncommutative geometry, analyzing black hole formation and naked singularities with new parameter insights.

Findings

Collapse can lead to black holes or naked singular shells depending on parameters.

Noncommutative corrections influence the evolution but do not prevent naked singularity formation.

Certain parameter regions favor noncommutative black hole formation before naked singular shells emerge.

Abstract

We study the formation of the (noncommutative) Schwarzschild black hole from collapsing shell {of the} generalized matters containing polytropic and Chaplygin gas. We show that this collapsing shell depending on various parameters forms either a black hole or a naked singular shell with the help of the pressure.Furthermore, by considering the smeared gravitational sources, we investigate the noncommutative black holes formation. Though this mild noncommutative correction of matters cannot ultimately resolve the emergence of the naked singularity, we show that in some parameter region the collapsing shell evolves to a noncommutative black hole before becoming a naked singular shell.