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We investigate the physics of black hole formation from the head-on collisions of boosted equal mass Oscillatons (OS) in full numerical relativity, for both the cases where the OS have equal phases or are maximally off-phase (anti-phase). While unboosted OS collisions will form a BH as long as their initial compactness $mathcal{C}equiv GM/R$ is above a numerically determined critical value $mathcal{C}>0.035$, we find that imparting a small initial boost counter-intuitively emph{prevents} the formation of black holes even if $mathcal{C}> 0.035$. If the boost is further increased, at very high boosts $gamma>1/12mathcal{C}$, BH formation occurs as predicted by the hoop conjecture. These two limits combine to form a stability band where collisions result in either the OS passing through (equal phase) or bouncing back (anti-phase), with a critical point occurring around ${cal C}approx 0.07$. We argue that the existence of this stability band can be explained by the competition between the free fall and the interaction timescales of the collision.
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The classical equations of motion for an axion with potential $V(phi)=m_a^2f_a^2 [1-cos (phi/f_a)]$ possess quasi-stable, localized, oscillating solutions, which we refer to as axion stars. We study, for the first time, collapse of axion stars numerically using the full non-linear Einstein equations of general relativity and the full non-perturbative cosine potential. We map regions on an axion star stability diagram, parameterized by the initial ADM mass, $M_{rm ADM}$, and axion decay constant, $f_a$. We identify three regions of the parameter space: i) long-lived oscillating axion star solutions, with a base frequency, $m_a$, modulated by self-interactions, ii) collapse to a BH and iii) complete dispersal due to gravitational cooling and interactions. We locate the boundaries of these three regions and an approximate triple point $(M_{rm TP},f_{rm TP})sim (2.4 M_{pl}^2/m_a,0.3 M_{pl})$. For $f_a$ below the triple point BH formation proceeds during winding (in the complex $U(1)$ picture) of the axion field near the dispersal phase. This could prevent astrophysical BH formation from axion stars with $f_all M_{pl}$. For larger $f_agtrsim f_{rm TP}$, BH formation occurs through the stable branch and we estimate the mass ratio of the BH to the stable state at the phase boundary to be $mathcal{O}(1)$ within numerical uncertainty. We discuss the observational relevance of our findings for axion stars as BH seeds, which are supermassive in the case of ultralight axions. For the QCD axion, the typical BH mass formed from axion star collapse is $M_{rm BH}sim 3.4 (f_a/0.6 M_{pl})^{1.2} M_odot$.
Primordial black holes (PBHs) are those which may have formed in the early Universe and affected the subsequent evolution of the Universe through their Hawking radiation and gravitational field. To constrain the early Universe from the observational constraint on the abundance of PBHs, it is essential to determine the formation threshold for primordial cosmological fluctuations, which are naturally described by cosmological long-wavelength solutions. I will briefly review our recent analytical and numerical results on the PBH formation.
We re-analyse current single-field inflationary models related to primordial black holes formation. We do so by taking into account recent developments on the estimations of their abundances and the influence of non-gaussianities. We show that, for all of them, the gaussian approximation, which is typically used to estimate the primordial black holes abundances, fails. However, in the case in which the inflaton potential has an inflection point, the contribution of non-gaussianities is only perturbative. Finally, we infer that only models featuring an inflection point in the inflationary potential, might predict, with a very good approximation, the desired abundances by the sole use of the gaussian statistics.
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 Zeldovich approximation, Thornes hoop conjecture, and Doroshkevichs probability distribution and subsequently derive the production probability $beta_{0}$ of primordial black holes. The numerical result obtained is applicable even if the density fluctuation $sigma$ at horizon entry is of the order of unity. For $sigmall 1$, we find a semi-analytic formula $beta_{0}simeq 0.05556 sigma^{5}$, 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 $sigmalesssim 0.05$, while they are comparable with each other for $sigmagtrsim 0.05$. We also discuss how $sigma$ can be written in terms of primordial curvature perturbations.
Primordial Black Holes (PBH) from peaks in the curvature power spectrum could constitute today an important fraction of the Dark Matter in the Universe. At horizon reentry, during the radiation era, order one fluctuations collapse gravitationally to form black holes and, at the same time, generate a stochastic background of gravitational waves coming from second order anisotropic stresses in matter. We study the amplitude and shape of this background for several phenomenological models of the curvature power spectrum that can be embedded in waterfall hybrid inflation, axion, domain wall, and boosts of PBH formation at the QCD transition. For a broad peak or a nearly scale invariant spectrum, this stochastic background is generically enhanced by about one order of magnitude, compared to a sharp feature. As a result, stellar-mass PBH from Gaussian fluctuations with a wide mass distribution are already in strong tension with the limits from Pulsar Timing Arrays, if they constitute a non negligible fraction of the Dark Matter. But this result is mitigated by the uncertainties on the curvature threshold leading to PBH formation. LISA will have the sensitivity to detect or rule out light PBH down to $10^{-14} M_{odot}$. Upcoming runs of LIGO/Virgo and future interferometers such as the Einstein Telescope will increase the frequency lever arm to constrain PBH from the QCD transition. Ultimately, the future SKA Pulsar Timing Arrays could probe the existence of even a single stellar-mass PBH in our Observable Universe.
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