arXiv subjects

Chul-Moon Yoo

Publications and source records attributed to Chul-Moon Yoo.

At least 37 records · Page 2Linked to original sources

arXiv2024

Revisiting spins of primordial black holes in a matter-dominated era based on peak theory

We estimate the probability distribution for the spins of the primordial black holes (PBHs) that formed during an early matter-dominated era in the Universe. We employ the Zel'dovich approximation and focus on the linear-order effect of cosmological perturbations which causes the tidal torque. Assuming that the fluctuations obey Gaussian statistics, we apply the peak theory of random Gaussian variables to compute the root mean square (RMS) and the probability distribution of the non-dimensional Kerr parameter $a_{*}$ at their formation. The value of $a_{*}$ is evaluated through the angular momentum at the turn-around time. We find that the RMS $\bar{a}_{*}$ with a given amplitude of the fluctuation $δ_{\rm{pk}}$ decreases with the amplitude. This behavior allows us to set the threshold value of the amplitude of the fluctuation through the under-extremal condition $\bar{a}_{*}<1$. Then we discuss the impact of spin and anisotropic collapse on the production rate of PBHs. We find that, for $σ_{H}\leq 10^{-3}$ with $σ_{\rm H}$ being the square root of the variance of the fluctuation at the horizon reentry, the suppression from the spin effect is dominant, while the effect of anisotropy becomes more important for $σ_{H}>10^{-3}$. Since $\bar{a}_{*}$ can be written as a function of $ν:=δ_{\rm{pk}}/σ_{\rm H}$, we can obtain the probability distribution of $\bar a_*$, $P(\bar a_*)$, through the probability distribution of $ν$ characterized by a given power spectrum of the fluctuation. $P(\bar a_*)$ depends on $σ_{\rm H}$ and the parameter $γ$ that characterizes the width of the power spectrum. It is shown that, in the parameter regions of our interests, substantial values of PBH spins are expected in contrast to the PBH formation in a radiation-dominated universe.

gr-qc↗

arXiv2024

Primordial Black Hole Formation from Type II Fluctuations with Primordial Non-Gaussianity

This study investigates the formation of primordial black holes (PBHs) resulting from the collapse of adiabatic fluctuations with large amplitudes and non-Gaussianity. Ref. \cite{Uehara:2024yyp} showed that fluctuations with large amplitudes lead to the formation of type B PBHs, characterized by the existence of the bifurcating trapping horizons, distinct from the more common type A PBHs without a bifurcating trapping horizon. We focus on the local type non-Gaussianity characterized by the curvature perturbation $ζ$ given by a function of a Gaussian random variable $ζ_{\rm G}$ as $βζ=-\ln(1-βζ_{\rm G})$ with a parameter $β$. Then we examine how the non-Gaussianity influences the dynamics and the type of PBH formed, particularly focusing on type II fluctuations, where the areal radius varies non-monotonically with the coordinate radius. Our findings indicate that, for $β>-2$, the threshold for distinguishing between type A and type B PBHs decreases with increasing $β$ similarly to the threshold for black hole formation. Additionally, for large positive values of $β$, the threshold for type B PBHs approaches that for type II fluctuations. We also find that, for a sufficiently large negative value of $β\lesssim-4.0$, the threshold value is in the type II region of $μ$, i.e., there are fluctuations of type II that do not form black holes. Lastly, we calculate the PBH mass for several values of $β$. Then we observe that the final mass monotonically increases with the initial amplitude within the parameter region of type A PBHs, which differs from previous analytical expectations.

gr-qc↗

arXiv2024

Primordial Black Holes and Induced Gravitational Waves from a Smooth Crossover beyond Standard Model

Gravitational waves (GWs) induced by primordial fluctuations can be affected by the modification of the sound speed $c^2_{\rm s}$ and the equation of state parameter $w$ once the curvature fluctuations reenter the cosmological horizon. That softening can also significantly boost the production of Primordial Black Holes (PBHs) at the mass scale where the softening arises. In this work, we consider a hypothetical softening of $w$ and $c^2_{\rm s}$ caused by a smooth crossover beyond Standard Model theories, for what we numerically compute the secondary induced GW considering the case of a flat scale-invariant power spectrum. We find that if the amplitude of the power spectrum is sufficiently large, the characteristic feature of the GW signal caused by the smooth crossover can be detected by future space-based gravitational wave interferometers and differentiated from the pure radiation case. At the same time, depending on the mass scale where the crossover occurs, such a scenario can have compatibility with PBHs being all the dark matter when $\mathcal{A} \sim \mathcal{O}(10^{-3})$, with a mass function very sharply peaked around the horizon mass scale of the minimum of the sound speed. Our results show that the GW signal can be used to resolve the existing degeneracy of sharply peaked mass function caused by peaked power spectrums and broad ones in the presence of softenings of $w$ and $c^2_{\rm s}$.

astro-ph.CO↗

arXiv2024

Primordial black hole formation from a nonspherical density profile with a misaligned deformation tensor

We perform the numerical simulation of primordial black hole formation from a nonspherical profile of the initial curvature perturbation $ζ$. We consider the background expanding universe filled with the perfect fluid with the linear equation of state $p=wρ$ ($w=1/3$ or $1/5$), where $p$ and $ρ$ are the pressure and the energy density, respectively. The initial condition is set in a way such that the principal directions of the second derivatives of $ζ$ and $\triangle ζ$ at the central peak are misaligned, where $\triangle$ is the Laplacian. In this setting, since the linearized density is proportional to $\triangle ζ$, the inertia tensor and deformation tensor $\partial_i\partial_j ζ$ are misaligned. Thus tidal torque may act and the spin of a resultant primordial black hole would be non-zero in general, although it is estimated to be very small from previous perturbative analyses. As a result, we do not find a finite value of the spin within our numerical precision, giving support for the negligibly small value of the black hole spin for $1/5\lesssim w \lesssim 1/3$. More specifically, our results suggest that the dimensionless PBH spin $s$ is typically so small that $s\ll0.1$ for $w\gtrsim0.2$.

gr-qc↗

arXiv2024

Abundance of Primordial Black Holes in Peak Theory for an Arbitrary Power Spectrum

We modify the procedure to estimate PBH abundance proposed in arXiv:1805.03946 so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure, we focus on peaks of the Laplacian of the curvature perturbation $\triangle ζ$ and use the values of $\triangle ζ$ and $\triangle \triangle ζ$ at each peak to specify the profile of $ζ$ as a function of the radial coordinate while the values of $ζ$ and $\triangle ζ$ are used in arXiv:1805.03946. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure in arXiv:1805.03946. Furthermore, the new procedure allows us to estimate PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the $k$-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the $k$-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.

astro-ph.CO↗

arXiv2024

The basics of primordial black hole formation and abundance estimation

This paper is a biased review of primordial black hole (PBH) formation and abundance estimation. We first review the three-zone model for PBH formation to help an intuitive understanding of the PBH formation process. Then, for more accurate analyses, we introduce necessary tools such as cosmological long-wavelength solutions, the definition of the mass and compaction function in a spherically symmetric spacetime and peak theory. Combining all these tools, we calculate the PBH mass spectrum for the case of the monochromatic curvature power spectrum as a demonstration.

astro-ph.CO↗

arXiv2024

Abundance of primordial black holes with local non-Gaussianity in peak theory

We discuss the effect of local type non-Gaussianity on the abundance of primordial black holes (PBH) based on the peak theory. We provide the PBH formation criterion based on the so-called compaction function and use the peak theory statistics associated with the curvature perturbation with the local type non-Gaussianity. Providing a method to estimate the PBH abundance, we demonstrate the effects of non-Gaussianity. It is explicitly shown that the value of non-linear parameter $|f_{\rm NL}| \sim 1$ induces a similar effect to a few factors of difference in the amplitude of the power spectrum.

astro-ph.CO↗

arXiv2024

PBH abundance from random Gaussian curvature perturbations and a local density threshold

The production rate of primordial black holes is often calculated by considering a nearly Gaussian distribution of cosmological perturbations, and assuming that black holes will form in regions where the amplitude of such perturbations exceeds a certain threshold. A threshold $ζ_{\rm th}$ for the curvature perturbation is somewhat inappropriate for this purpose, because it depends significantly on environmental effects, not essential to the local dynamics. By contrast, a threshold $δ_{\rm th}$ for the density perturbation at horizon crossing seems to provide a more robust criterion. On the other hand, the density perturbation is known to be bounded above by a maximum limit $δ_{\rm max}$, and given that $δ_{\rm th}$ is comparable to $δ_{\rm max}$, the density perturbation will be far from Gaussian near or above the threshold. In this paper, we provide a new plausible estimate for the primordial black hole abundance based on peak theory. In our approach, we assume that the curvature perturbation is given as a random Gaussian field with the power spectrum characterized by a single scale, while an optimized criterion for PBH formation is imposed, based on the locally averaged density perturbation. Both variables are related by the full nonlinear expression derived in the long-wavelength approximation of general relativity. We do not introduce a window function, and the scale of the inhomogeneity is introduced as a random variable in the peak theory. We find that the mass spectrum is shifted to larger mass scales by one order of magnitude or so, compared to a conventional calculation. The abundance of PBHs becomes significantly larger than the conventional one, by many orders of magnitude, mainly due to the optimized criterion for PBH formation and the removal of the suppresion associated with a window function.

astro-ph.CO↗

arXiv2024

Primordial Black Hole formation from overlapping cosmological fluctuations

We consider the formation of primordial black holes (PBHs), during the radiation-dominated Universe, generated from the collapse of super-horizon curvature fluctuations that are overlapped with others on larger scales. Using a set of different curvature profiles, we show that the threshold for PBH formation (defined as the critical peak of the compaction function) can be decreased by several percentages, thanks to the overlapping between two peaks in the profile of the compaction function. In the opposite case, when the fluctuations are sufficiently decoupled the threshold values behave as having the fluctuations isolated (isolated peaks). We find that the analytical estimates of arXiv:1907.13311 can be used accurately when applied to the corresponding peak that is leading to the gravitational collapse. We also study in detail the dynamics and estimate the final PBH mass for different initial configurations, showing that the profile dependence has a significant effect on that.

gr-qc↗

arXiv2024

Turbulence on open string worldsheets under non-integrable boundary conditions

We demonstrate the turbulent dynamics of the Nambu-Goto open string in the AdS3 spacetime. While the motion of a classical closed string in AdS is known to be integrable, the integrability of an open string motion depends on the boundary conditions at the string endpoints. We numerically solve the equations of motion of the open string under the boundary conditions where the endpoints are i) fixed to a finite radial coordinate in AdS, and ii) free. For i), we find turbulence on the string, that shows a cascade in the energy and angular momentum spectra. This result indicates the non-integrability of the open string with this type of boundary conditions. For ii), we find no turbulence. This is consistent with the integrability of the open string with the free boundary conditions.

hep-th↗

arXiv2023

Axion Cloud Decay due to the Axion-photon Conversion with Multi-pole Background Magnetic Fields

We consider axion cloud decay due to the axion-photon conversion with multi-pole background magnetic fields. We focus on the $\ell=m=1$ and $n=2$ mode for the axion field configuration since it has the largest growth rate associated with superradiant instability. Under the existence of a background multi-pole magnetic field, the axion field can be converted into the electromagnetic field through the axion-photon coupling. Then the decay rate due to the dissipation of the converted photons is calculated in a successive approximation. We found that the decay rate is significantly dependent on the azimuthal quantum number characterizing the background magnetic field, and can be comparable to or larger than the growth rate of the superradiant instability.

hep-ph↗

arXiv2023

Revisiting compaction functions for primordial black hole formation

Shibata and Sasaki [arXiv:gr-qc/9905064] introduced the so-called compaction function. Since then, it has been empirically established that the maximum value of this function (or its volume-averaged counterpart) in the long-wavelength solutions gives a very robust threshold of primordial black hole formation. In this paper, we show that in spite of initial intention, the Shibata-Sasaki compaction function cannot be interpreted as the ratio of the mass excess to the areal radius in the constant-mean-curvature slice of their choice but coincides with that in the {\it comoving} slice up to a constant factor depending on the equation of state. We also discuss the gauge-(in)dependence of the legitimate compaction function, i.e., the ratio of the mass excess to the areal radius, in the long-wavelength solutions.

gr-qc↗

arXiv2023

Spins of primordial black holes formed with a soft equation of state

We investigate the probability distribution of the spins of primordial black holes (PBHs) formed in the universe dominated by a perfect fluid with the linear equation of state $p=wρ$, where $p$ and $ρ$ are the pressure and energy density of the fluid, respectively. We particularly focus on the parameter region $0<w\leq 1/3$ since the larger value of the spin is expected for the softer equation of state than that of the radiation fluid ($w=1/3$). The angular momentum inside the collapsing region is estimated based on the linear perturbation equation at the turn-around time which we define as the time when the linear velocity perturbation in the conformal Newtonian gauge takes the minimum value. The probability distribution is derived based on the peak theory with the Gaussian curvature perturbation. We find that the root mean square of the non-dimensional Kerr parameter $\sqrt{\langle a_{*}^2\rangle}$ is approximately proportional to $(M/M_{H})^{-1/3}(6w)^{-(1+2w)/(1+3w)}$, where $M$ and $M_{H}$ are the mass of the PBH and the horizon mass at the horizon entry, respectively. Therefore the typical value of the spin parameter decreases with the value of $w$. We also evaluate the mass and spin distribution $P(a_{*}, M)$, taking account of the critical phenomena. We find that, while the spin is mostly distributed in the range of $10^{-3.9}\leq a_{*}\leq 10^{-1.8}$ for the radiation-dominated universe, the peak of the spin distribution is shifted to the larger range $10^{-3.0}\leq a_{*}\leq 10^{-0.7}$ for $w=10^{-3}$.

gr-qc↗

arXiv2023

Stationary Vacuum Bubble in a Kerr-de Sitter Spacetime

We study false vacuum decay in a black hole (BH) spacetime with an angular momentum. Considering the false vacuum region described by a Kerr-de Sitter geometry, under the thin wall approximation, we can obtain the stationary configuration of the vacuum bubble seen from the outside false vacuum region without specifying the geometry inside the domain wall. Then, assuming the true vacuum region is described by a Kerr geometry, we can fix the mass and the spin parameter for the Kerr geometry by imposing the 1st junction conditions and conservation of the angular momentum. Although the assumption of the Kerr geometry inside the domain wall cannot be fully consistent with the 2nd junction conditions, we can roughly evaluate the error associated with this inconsistency by calculating the Brown-York quasi-local energy on the domain wall. Then the decay rate can be estimated by using the obtained parameters for the inside Kerr geometry and the Brown-York quasi-local energy. Our results support the statement that the BH spin suppresses the false vacuum decay in a BH spacetime.

gr-qc↗

arXiv2023

Einstein-Vlasov system with equal-angular momenta in $\text{AdS}_5$

We investigate solutions of the $5$--dimensional rotating Einstein-Vlasov system with an $R \times SU(2) \times U(1)$ isometry group. In a five-dimensional spacetime, there are two independent planes of rotation, thus, considering $U(1)$ symmetry on each rotation plane, we may impose an $R\times U(1) \times U(1)$ isometry to a stationary spacetime. Furthermore, when the values of the two angular momenta are equal to each other, the spatial symmetry gets enhanced to $R\times SU(2)\times U(1)$ symmetry, and the spacetime has a cohomogeneity-1 structure. Imposing the same symmetry to the distribution function of the particles of which the Vlasov system consists, the distribution function can be dependent on three mutually independent and commutative conserved charges for particle motion (energy, total angular momentum on $SU(2)$ and $U(1)$ angular momentum). We consider the distribution function which exponentially depends on the $U(1)$ angular momentum and reduces to the thermal equilibrium state in spherical symmetry. Then, in this paper, we numerically construct solutions of the asymptotically AdS Einstein--Vlasov system.

gr-qc↗

arXiv2023

Threshold of Primordial Black Hole Formation in Nonspherical Collapse

We perform (3+1)-dimensional simulations of primordial black hole (PBH) formation starting from the spheroidal super-horizon perturbations. We investigate how the ellipticity (prolateness or oblateness) affects the threshold of PBH formation in terms of the peak amplitude of curvature perturbation. We find that, in the case of the radiation-dominated universe, the effect of ellipticity on the threshold is negligibly small for the large amplitude of perturbations expected for PBH formation.

gr-qc↗

arXiv2023

Threshold of Primordial Black Hole Formation against Velocity Dispersion in Matter-Dominated Era

We study the effects of velocity dispersion on the formation of primordial black holes~(PBHs) in a matter-dominated era. The velocity dispersion is generated through the nonlinear growth of perturbations and has the potential to impede the gravitational collapse and thereby the formation of PBHs. To make discussions clear, we consider two distinct length scales. The larger one is where gravitational collapse occurs which could lead to PBH formation, and the smaller one is where the velocity dispersion develops due to nonlinear interactions. We estimate the effect of the velocity dispersion on the PBH formation by comparing the free-fall timescale and the timescale for a particle to cross the collapsing region. As a demonstration, we consider a log-normal power spectrum for the initial density perturbation with the peak value $σ_0^2$ at a scale that corresponds to the larger scale. We find that the threshold value of the density perturbation $\tilde δ_{\rm th}$ at the horizon entry for the PBH formation scales as $\tilde δ_{\rm th}\propto σ_0^{2/5}$ for $σ_0\ll1$.

astro-ph.CO↗

arXiv2022

Gravothermal catastrophe and critical dimension in a $D$-dimensional asymptotically AdS spacetime

We investigate the structure and stability of the thermal equilibrium states of a spherically symmetric self-gravitating system in a $D$-dimensional asymptotically Anti-de Sitter(AdS) spacetime. The system satisfies the Einstein-Vlasov equations with a negative cosmological constant. Due to the confined structure of the AdS potential, we can construct thermal equilibrium states without any artificial wall in the asymptotically AdS spacetime. Accordingly, the AdS radius can be regarded as the typical size of the system. Then the system can be characterized by the gravothermal energy and AdS radius normalized by the total particle number. We investigate the catastrophic instability of the system in a $D$-dimensional spacetime by using the turning point method. As a result, we find that the curve has a double spiral structure for $4\le D\le 10$ while it does not have any spiral structures for $D\ge11$ as in the asymptotically flat case confined by an adiabatic wall. Irrespective of the existence of the spiral structure, there exist upper and lower bounds for the value of the gravothermal energy. This fact indicates that there is no thermal equilibrium solution outside the allowed region of the gravothermal energy. This property is also similar to the asymptotically flat case.

gr-qc↗