arXiv subjects

Daiki Saito

Publications and source records attributed to Daiki Saito.

18 recordsLinked to original sources

arXiv2026

Anisotropic separate universe : Long-wavelength perturbations and conserved quantities

We investigate the long-wavelength evolution of linear perturbations in a homogeneous and anisotropic background with a scalar field coupled to a vector field. Using the spatial gradient expansion in the uniform-$\mathcal{N}$ gauge in which the number of $e$-folds is unperturbed, we derive the complete set of superhorizon solutions and establish their correspondence with infinitesimal variations of the homogeneous anisotropic background. This extends the separate-universe picture, previously known for isotropic FLRW cosmology, to anisotropic spacetimes despite the mixing of scalar, vector, and tensor perturbations induced by broken rotational symmetry. We show that the long-wavelength equations form a self-consistent system and identify a conserved quantity that generalizes the conserved Wronskian of isotropic cosmology. Unlike the isotropic case, the superhorizon modes sourcing the curvature perturbation are governed by three independent conserved channels associated with the scalar field, the background shear, and the gauge-field tilt, together with an additional dynamical shear contribution originating from the anisotropic geometry. This reveals that the evolution of curvature perturbations around anisotropic background is intrinsically richer than in isotropic multi-field models. Our formulation provides a practical prescription for computing the final curvature perturbation directly from horizon-crossing fluctuations, thereby establishing the anisotropic generalization of the $\delta N$ formalism. We further derive an explicit relation between curvature perturbations and primordial gravitational waves, demonstrating how anisotropic expansion couples scalar and tensor sectors on superhorizon scales. Our framework provides a practical basis for predicting statistical anisotropies in primordial scalar and tensor perturbations.

astro-ph.CO↗

arXiv2026

Refocusing of Wheeler--DeWitt wave functions at inner horizons

We study quantum gravitational effects inside hyperbolic black holes with both outer and inner horizons by solving the Wheeler--DeWitt (WDW) equation in the minisuperspace approximation. The WDW equation contains a tachyonic region where the effective potential becomes negative. We develop a numerical method that consistently evolves the wave function across this region and obtain stable solutions throughout the entire minisuperspace. For small values of the parameter $\kappa$, which controls the strength of quantum gravitational effects, the wave packet propagates along the classical trajectory with only mild quantum spreading. As $\kappa$ increases, enhanced quantum effects lead to significant spreading of the wave packet during its propagation. Nevertheless, when the initial state is localized near the outer horizon, the wave packet becomes localized again in the vicinity of the inner horizon. We refer to this recovery of localization as a refocusing phenomenon. This result suggests that, if the geometry is classical near the outer horizon, it becomes classical again near the inner horizon. Within the minisuperspace approximation, inner-horizon formation is not obstructed by quantum gravitational effects.

gr-qc↗

arXiv2026

COSMOS: A numerical relativity code specialized for PBH formation

Primordial black holes (PBHs) are black holes generated in the early universe without having gone through stellar evolution. In the standard formation process, PBHs are formed from super-horizon primordial fluctuations with non-linearly large initial amplitude. In order to simulate the non-linear gravitational dynamics of PBH formation, one has to rely on numerical relativity solvers to approximate the solution of the Einstein equations. COSMOS is a C++ package for solving the Einstein equations in 3+1 dimensions, providing simple tools for the simulation of PBH formation. In order to resolve the collapsing region, non-Cartesian scale-up coordinates and a fixed mesh-refinement procedure are implemented. In COSMOS, a massless scalar field and a perfect fluid with a linear equation of state are implemented as matter fields. To achieve a practically acceptable computational speed, OpenMP is used for the parallelization. COSMOS has no other dependencies, which makes for an easier installation.

gr-qc↗

arXiv2026

Primordial black holes in excursion set theory: Formation probabilities, mass functions, and window functions

We study the mass function of primordial black holes (PBHs) within the excursion-set theory, in which the response of the stochastic density contrast to the variation of the coarse-graining scale is described by colored noises. For several window functions often used in the literature, we investigate how this choice affects the formation probability as well as the resultant mass function of PBHs. It is found that the low-mass tail of the mass function differs from the one predicted from Carr's formula. The difference comes from the prevalence of correlated noises, by which degeneracy of the formation probabilities ceases to exist. Nevertheless, Carr's formula still provides a practical estimation in the vicinity of the characteristic mass scale, as long as a smooth window function in Fourier space is used.

astro-ph.CO↗

arXiv2026

Rotating wormholes in five dimensions with equal angular momenta: large asymmetry regime

We clarify the relationship between rotation and the energy condition for stationary rotating wormhole solutions of the Einstein equations coupled to a phantom field in five-dimensional spacetime with equal angular momenta, particularly with large asymmetry between the two sides. It was shown by Dzhunushaliev et al. that the violation of the null energy condition can become arbitrarily small due to rotation. We find that the degree of violation of the null energy condition is essentially determined by the angular momentum and shows little dependence on asymmetry, that is, the mass difference between the two asymptotic regions. We also discuss the relation between the wormhole spacetime and the Myers-Perry black hole. We find that the geometry asymptotes to the extremal Myers-Perry spacetime in the limit of large angular momentum, while the non-extremal black hole geometry cannot be reproduced in any limit.

gr-qc↗

arXiv2026

Dynamical Formation of Self-Similar Wormholes

We study spherically symmetric, self-similar wormhole solutions supported by colliding streams of negative-energy null dust, and their dynamical formation. Under the assumption of self-similarity, the Einstein equations reduce to a system of ordinary differential equations, which we solve numerically under boundary conditions enforcing the existence of a minimal areal radius (the throat) on constant-time hypersurfaces. For a sufficiently large throat radius, the resulting geometries remain regular at both spatial and future null infinity, while a singularity is retained in the past direction. We then construct a dynamical formation scenario by patching together three regions: a Schwarzschild black hole, negative-energy Vaidya spacetimes, and the self-similar wormhole geometry. These regions are joined across null shells using the Barrabes--Israel formalism, which provides explicit relations among the throat radius, the black hole's mass and the energy injection by the shell, demonstrating that an initial black hole can evolve into a wormhole. Our analysis generalizes the formation model for static wormhole solutions proposed by Hayward and Koyama in 2004 to non-static wormhole solutions, offering a novel perspective on the formation of regular traversable wormholes.

gr-qc↗

arXiv2025

Primordial black holes and smooth coarse-graining in excursion set theory

The excursion-set formalism enables us to infer the mass distribution of collapsed objects, such as primordial black holes (PBHs), by the language of stochastic processes. Within the framework, this article investigates how a smooth coarse-graining procedure affects the resulting PBH mass function. As a demonstrative example, we employ a Gaussian window function, for which the stochastic noise becomes fully correlated across scales. It is found that these correlated noises result in a mass function of PBHs, whose maximum and its neighbourhood are predominantly determined by the probability that the density contrast exceeds a given threshold at each mass scale. Our results clarify the role of noise correlations induced by smooth coarse-graining and highlight their importance in predicting the abundance of PBHs.

astro-ph.CO↗

arXiv2025

Numerical simulation of type II primordial black hole formation

This study investigates the formation of type II primordial black holes (PBHs) resulting from extremely large amplitudes of initial fluctuations in a radiation-dominated universe. We find that, for a sufficiently large initial amplitude, the configuration of trapping horizons shows characteristic structure due to the existence of bifurcating trapping horizons. We call this type of configuration of the trapping horizons type II-B PBH, while the structure without a bifurcating trapping horizon type II-A PBH. In Ref. [1], in the dust-dominated universe, the type B PBH can be realized by the type II initial fluctuation, which is characterized by a non-monotonic areal radius as a function of the radial coordinate (throat structure) in contrast with the standard case, type A PBH with a monotonic areal radius (type I fluctuation). Our research reveals that a type II fluctuation does not necessarily result in a type B PBH in the radiation-dominated case. We also find that for an initial amplitude well above the threshold value, the resulting PBH mass may either increase or decrease with the initial amplitude, depending on its specific profile rather than its fluctuation type.

gr-qc↗

arXiv2025

Primordial Black Hole Formation and Spin in Matter Domination Revisited

In this article, we calculate the mass distribution of primordial black holes (PBHs) formed in the matter-dominated (MD) era by the peak theory. We apply the Zel'dovich approximation to track the nonlinear evolution of overdensities and compute the PBH abundance and mass function by incorporating a PBH formation criterion based on the hoop conjecture. We find that the PBH abundance $β$ follows the scaling law $β\simeq A_γσ_h^{*5}$ for $σ_h^*\ll 1$. Here, $σ_h^*$ is the quantity that characterizes the variance of the density fluctuation at the horizon entry. We also find that, in contrast to the previous estimates, the PBH spin is very small for $σ_h^*\ll 1$ but could be larger for larger $σ_h^*$ and broader power spectra. Finally, specializing to a monochromatic power spectrum, we prove analytically that the PBH mass distribution becomes effectively monochromatic and reveal that the resultant PBH abundance is approximately 19 times the previous prediction.

gr-qc↗

arXiv2025

Dynamical Formation of Charged Wormholes

We construct static, spherically symmetric, charged traversable wormhole solutions to the Einstein--Maxwell equations, supported by bidirectional (ingoing and outgoing) null dust with negative energy, and discuss a scenario for their dynamical formation from a black hole. Our solution contains a traversable throat, where the areal radius takes a minimum, although the spacetime is not asymptotically flat. In our formation scenario, the spacetime evolves sequentially from a black hole to Vaidya regions and finally to a wormhole, with each transition mediated by an impulsive null shell. We find that the radius of the wormhole throat is determined by the mass and charge of the initial black hole as well as those of the injected shell.

gr-qc↗

arXiv2025

Primordial black hole formation from a type II perturbation in the absence and presence of pressure

We investigate primordial black holes (PBHs) formed from extremely large amplitudes of primordial curvature fluctuations, classified as type II. Type II fluctuations differ from type I by the presence of a stationary point on the initial time slice, when we see the areal radius as a function of the radial coordinate. Starting from these type II perturbations to form black holes, the nonlinear evolution governed by the Einstein equations generally results in two distinct types, A and B, of horizon configurations, respectively characterized by the absence and presence of a bifurcating trapping horizon where past and future trapping horizons meet. In this paper, we use the Lemaitre-Tolman-Bondi solution to show that type I/II and type A/B classifications are equivalent for a spherically symmetric dust fluid system, regardless of the fluctuation profile. However, this equivalence does not generally hold in the presence of pressure.

gr-qc↗

arXiv2025

Remote Hawking-Moss instanton and the Lorentzian path integral

The Hawking-Moss (HM) bounce solution implies that the tunneling amplitude between vacua is uniquely determined by the vacuum energy at the initial vacuum and the top of a potential barrier, regardless of the field distance between them $Δϕ$. This implausible conclusion was carefully discussed in [E. J. Weinberg, Phys. Rev. Lett. 98, 251303, (2007)], and it was concluded that the conventional HM amplitude is not reliable for a transition to the top of distant local maxima (hereinafter referred to as the remote HM transition). We revisit this issue and study the impact of the quantum tunneling effect on the remote HM transition. We demonstrate that the amplitude for such a distant transition is indeed smaller than the conventional HM amplitude by employing the Lorentzian path integral in a simple setup. We consider a linear potential, which allows for analytic treatments, and evaluate the up-tunneling probability of a homogeneous scalar field in de Sitter spacetime. The Picard-Lefschetz theory is employed to identify the relevant Lefschetz thimble, representing the relevant tunneling trajectory. We then compare the resulting transition amplitude with the conventional HM amplitude. We find that when the field separation $|Δϕ|$ is larger, the quantum-tunneling amplitude, estimated by our Lorentzian path integral, is smaller than that of the conventional HM amplitude. This implies that the transition amplitude may be significantly suppressed if the thermal interpretation is not applicable and the quantum-tunneling effect is dominant for the remote HM transition.

hep-th↗

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

Removing naked singularities in static axially symmetric spacetimes by patching with the flat spacetimes

We investigate static, axially symmetric spacetimes without naked singularities that are constructed by patching Weyl class spacetimes with the flat spacetimes. Once the exterior geometry is specified, the junction conditions determine the shape of a thin shell, which is the boundary between the two patched spacetimes, and the distribution of the energy and pressure on this shell, leaving a parameter representing the shell size free. We examine the cases where the exterior of the shell is given by Curzon--Chazy or Zipoy--Voorhees spacetimes. For each case, we find a lower bound on the shell size. Additionally, we find that the weak and null energy conditions are satisfied for any shell size, while the dominant energy condition is satisfied for sufficiently large shells. These results provide concrete examples of non-singular spacetimes with non-spherically symmetric exteriors that respect the energy conditions.

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↗

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↗

arXiv2021

False Vacuum Decay in Rotating BTZ Spacetimes

We analyse vacuum decay in rotating BTZ black hole spacetimes with the thin wall approximation. Possible parameter regions for the vacuum decay are clarified. We find that the nucleation rate is dominated by the bounce solution with the static shell configuration. The nucleation rate of the static shell decreases with the mass of the initial black hole. For a larger/smaller value of the initial black hole, the nucleation rate can be smaller/larger than that of the Coleman De Luccia vacuum decay in the pure AdS spacetime. Through the vacuum decay, the black hole gains its mass and loses the horizon area. We also find that the nucleation rate increases with increasing the angular momentum of the spacetime.

gr-qc↗