Instability of black hole formation under small pressure perturbations

TL;DR

This paper demonstrates that introducing even tiny perfect fluid pressures into classical black hole collapse models can alter the outcome, often resulting in naked singularities instead of black holes, highlighting the sensitivity of collapse outcomes.

Contribution

It extends previous work on pressure effects in gravitational collapse to perfect fluids, showing that small perturbations can change the endstate from black hole to naked singularity.

Findings

Small pressure perturbations can prevent black hole formation.

Any neighborhood of the OSD model contains evolutions leading to naked singularities.

Naked singularities can form from arbitrarily small pressure changes.

Abstract

We investigate here the spectrum of gravitational collapse endstates when arbitrarily small perfect fluid pressures are introduced in the classic black hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD) [1]. This extends a previous result on tangential pressures [2] to the more physically realistic scenario of perfect fluid collapse. The existence of classes of pressure perturbations is shown explicitly, which has the property that injecting any smallest pressure changes the final fate of the dynamical collapse from a black hole to a naked singularity. It is therefore seen that any smallest neighborhood of the OSD model, in the space of initial data, contains collapse evolutions that go to a naked singularity outcome. This gives an intriguing insight on the nature of naked singularity formation in gravitational collapse.