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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 $M_{rm BH}sim 3.4 (f_a/0.6 M_{pl})^{1.2} M_odot$.
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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.
Axions and axion-like particles are compelling candidates for the missing dark matter of the universe. As they undergo gravitational collapse, they can form compact objects such as axion stars or even black holes. In this paper, we study the formation and distribution of such objects. First, we simulate the formation of compact axion stars using numerical relativity with aspherical initial conditions that could represent the final stages of axion dark matter structure formation. We show that the final states of such collapse closely follow the known relationship of initial mass and axion decay constant $f_a$. Second, we demonstrate with a toy model how this information can be used to scan a model density field to predict the number densities and masses of such compact objects. In addition to being detectable by the LIGO/VIRGO gravitational wave interferometer network for axion mass of $10^{-9} < m_a < 10^{-11}$ eV, we show using peak statistics that for $f_a < 0.2M_{pl}$, there exists a mass gap between the masses of axion stars and black holes formed from collapse.
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.
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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