Horizonless, singularity-free, compact shells satisfying NEC

TL;DR

This paper explores how, in a modified gravity theory with torsion, matter can be compressed into arbitrarily small, non-singular shells satisfying the null energy condition, challenging traditional singularity formation in gravitational collapse.

Contribution

It demonstrates the existence of horizonless, singularity-free compact shells satisfying NEC in a modified gravity framework with torsion, expanding possibilities beyond classical black hole models.

Findings

Matter can be collapsed arbitrarily small without singularities.

High pressure allows collapse while satisfying NEC.

Solutions are static shells in a modified gravity context.

Abstract

Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition collapses to the extent a closed trapped surface is formed, a singularity is inevitable according to Penrose's singularity theorem. Since positive mass vacuum solutions are generally black holes with trapped surfaces inside the event horizon, matter cannot collapse to an arbitrarily small size without generating a singularity. However, in modified theories of gravity where positive mass vacuum solutions are naked singularities with no trapped surfaces, it is reasonable to expect that matter can collapse to an arbitrarily small size without generating a singularity. Here we examine this possibility in the context of a modified theory of gravity with torsion in an extra dimension. We study singularity-free static shell solutions to evaluate the validity of the null energy condition on the shell. We find that with sufficiently high pressure, matter can be collapsed to arbitrarily small size without violating the null energy condition and without producing a singularity.