The impact of the eccentricity on the collapse of an ellipsoid into a black hole

TL;DR

This paper investigates how the initial eccentricity of a homogeneous pressureless ellipsoid influences its gravitational collapse into a black hole, revealing a universal power-law relationship and estimating conditions for direct black hole formation.

Contribution

It introduces a universal power-law dependence of minimal collapse size on initial eccentricity and estimates parameters for direct black hole formation from collapse.

Findings

Minimal size during collapse scales as e_0^{15/8}

Dependence on eccentricity is highly universal

Parameters for direct black hole formation are estimated

Abstract

We consider the gravitational collapse of a homogeneous pressureless ellipsoid. We have shown that the minimal size $r$ that the ellipsoid can reach during collapse depends on its initial eccentricity $e_0$ as $r\propto e_0^\nu$, where $\nu \approx 15/8$, and this dependence is very universal. We have estimated the parameters (in particular, the initial eccentricity) of a homogeneous pressureless ellipsoid, whereat it collapses directly into a black hole.