Primordial Black Hole Formation in the Matter-Dominated Phase of the Universe

Abstract

We investigate primordial black hole formation in the matter-dominated phase of the Universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zel'dovich approximation, Thorne's hoop conjecture, and Doroshkevich's probability distribution and subsequently derive the production probability β 0 of primordial black holes. The numerical result obtained is applicable even if the density fluctuation σ at horizon entry is of the order of unity. For σ 1, we find a semi-analytic formula β 0 0.05556σ 5 , which is comparable with the Khlopov-Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for σ 0.05, while they are comparable with each other for σ 0.05. We also discuss how σ can be written in terms of primordial curvature perturbations.

Spins of primordial black holes formed in the matter-dominated phase of the Universe

“…We have z 0 (t, u) = z * (t, u) for −1 − (2/3)u < t < 0 and t 1 (u) < t < t 2 (u), while z 0 (t, u) = z th (t) for 0 < t < t 1 (u) and t 2 (u) < t. The integration with respect to z can be done explicitly using a well-known formula, which is given by Eq. (66) in Appendix A of [30]. The result is…”

“…and E(e) is the complete elliptic integral of the second kind [30]. The production rate P ai due to this effect is calculated by…”

“…It would be interesting to calculate the probability of black hole formation by combining the effects of angular momentum and anisotropic collapse, the latter of which has been studied by Khlopov and Polnarev [25,26] and refined by Harada et al [30].…”

“…Harada et al [30] reanalyzed this problem and found that the application of the hoop conjecture for black hole formation results in the production rate β 0 ≃ 0.05556σ 5 H for σ H ≪ 1. Based on this estimate of the production rate, Carr et al [31] discussed the inflaton and spectator field perturbations.…”

Primordial black holes and Co-Decaying dark matter

“…In this paper, we will use the Zel'dovich Approximation [43,44] to estimate the abundance of PBHs. This method has been used by a number of authors to estimate PBH production in an EMDE [42][43][44][45][46][47] -and more recently in [13,14,[48][49][50]. The approximation has been shown to be in good agreement with full N-body simulations until the time of shell-crossing (caustic formation) [51] and we leave a full N-body simulation to future work.…”