Simulations of Ellipsoidal Primordial Black Hole Formation

TL;DR

This study uses 3+1 relativistic simulations to analyze how non-spherical perturbations influence primordial black hole formation, revealing critical thresholds and the impact of ellipticity on collapse outcomes.

Contribution

It provides the first detailed numerical analysis of the effects of ellipticity and prolateness on PBH formation thresholds in a relativistic framework.

Findings

Critical non-spherical parameters follow a superellipse curve.

Small deviations from sphericity can prevent collapse near the threshold.

Ellipticity significantly affects the PBH production rate.

Abstract

We perform $3+1$ relativistic numerical simulations to study primordial black hole (PBH) formation from the collapse of adiabatic super-horizon non-spherical perturbations generated from curvature fluctuations obeying random Gaussian statistics with a monochromatic power spectrum. The matter field is assumed to be a perfect fluid of an equation of state $w:=P/\rho={\rm const.}$ with $P$ and $\rho$ being the pressure and the energy density, respectively. The initial spatial profile of the curvature perturbation is modeled with the amplitude $\mu$ and non-spherical parameters $e$ (ellipticity) and $p$ (prolateness) according to peak theory. We focus on the dynamics and the threshold for PBH formation in terms of the non-spherical parameters $e$ and $p$. We find that the critical values ($e_c, p_c$) with a fixed value of $\mu$ closely follow a superellipse curve. With $p=0$, for the range of amplitudes considered, we find that the critical ellipticity for non-spherical collapse follows a decaying power law as a function of $(\mu-\mu_{\rm c,sp})$ with $\mu_{\rm c,sp}$ being the threshold for the spherical case. Our results also indicate that, for both cases of $w = 1/3$ and $w = 1/10$, small deviations from sphericity can avoid collapsing to a black hole when the amplitude is near its critical threshold. Finally we discuss the significance of the ellipticity on the rate of the PBH production.