Primordial black hole formation with full numerical relativity

Abstract: We study the formation of black holes from subhorizon and superhorizon perturbations in a matter dominated universe with 3+1D numerical relativity simulations. We find that there are two primary mechanisms of formation depending on the initial perturbation's mass and geometry -- via $\textit{direct collapse}$ of the initial overdensity and via $\textit{post-collapse accretion}$ of the ambient dark matter. In particular, for the latter case, the initial perturbation does not have to satisfy the hoop conjecture for a black hole to form. In both cases, the duration of the formation the process is around a Hubble time, and the initial mass of the black hole is $M_\mathrm{BH} \sim 10^{-2} H^{-1} M_\mathrm{Pl}^2$. Post formation, we find that the PBH undergoes rapid mass growth beyond the self-similar limit $M_\mathrm{BH}\propto H^{-1}$, at least initially. We argue that this implies that most of the final mass of the PBH is accreted from its ambient surroundings post formation.

• The paper demonstrates that direct collapse and subsequent accretion drive primordial black hole formation, with initial masses around 10⁻² of the Hubble scale.
• It employs 3+1D numerical relativity to model non-linear perturbations from massive and massless scalar fields over approximately one Hubble time.
• The findings reveal strong deviations from linear growth predictions, emphasizing how initial perturbation geometry critically influences PBH mass accretion and cosmological implications.

Primordial Black Hole Formation with Full Numerical Relativity

The study "Primordial Black Hole Formation with Full Numerical Relativity" provides a comprehensive analysis of the formation mechanisms of primordial black holes (PBHs) through the use of 3+1D numerical relativity simulations in a universe dominated by matter. This research focuses on two primary methods of PBH formation: direct collapse and accretion-driven collapse, influenced by the initial perturbation characteristics of mass and geometry.

Summary of Methodology and Findings

The authors engage 3+1D numerical relativity simulations to examine the collapse of non-linear perturbations originating both inside and outside the horizon in a matter-dominated cosmological model. Here, a massive scalar field represents dark matter, and a massless scalar field generates the initial perturbations. These perturbations facilitate black hole formation through either direct collapse or subsequent accretion of dark matter from the environment. The simulations reveal the duration of these processes to be approximately one Hubble time, leading to initial PBH masses on the order of $10^{-2}$ times the Hubble scale in Planck units.

Mechanisms of PBH Formation

1. Direct Collapse: This mechanism involves the immediate black hole formation from a superhorizon perturbation without significant interaction with surrounding dark matter. The conditions favoring direct collapse align with predictions from the hoop conjecture, asserting that the perturbation’s geometry plays a decisive role.
2. Accretion-Driven Collapse: For perturbations that fail to achieve black hole status independently, subsequent accretion of ambient dark matter is instrumental. The authors show that the accretion rate surpasses linear predictions, with substantial mass growth occurring post-collapse, often exceeding the initial self-similar limits.

The simulations suggest that strong deviations from simple linear growth models occur, underlining the complex interplay between the growth rates and the geometry of the initial perturbations. This accretion process promises significant implications for the final masses of PBHs, indicating most mass accrual occurs following the initial PBH formation.

Implications and Future Prospects

This study provides essential insights for improving the theoretical understanding of PBH formation, particularly during epochs dominated by matter. The findings bear substantial potential to inform constraints on the abundance and mass distribution of PBHs, with implications for scenarios where they contribute to dark matter or seed supermassive black holes.

In terms of observational prospects, the scenarios postulated in this paper align with expectations for early universe cosmologies prior to Big Bang Nucleosynthesis (BBN). Given the proposed mass growth mechanisms, PBHs formed at energy scales relevant to BBN potentially align with mass ranges measurable by current and future gravitational wave observatories. These instruments could thus validate the presence of PBHs and their role in pivotal cosmic processes.

Furthermore, the paper’s methodological framework highlights the necessity for future numerical simulations to capture the full scope of PBH formation mechanisms across varied cosmological conditions. Subsequent investigations could explore extended parameter spaces, including less symmetric configurations, offering further understanding of PBH formation conditions.

In conclusion, this research presents a detailed numerical study on PBH formation, emphasizing mechanisms most active under matter domination, and setting the stage for expanded theoretical and observational explorations of primordial black holes in cosmological settings.