Simulations of Ellipsoidal Primordial Black Hole Formation

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.

;Comment: 31 pages, 24 figures.

v2: references added and minor typographical typos corrected