arXiv subjects

Hayato Motohashi

Publications and source records attributed to Hayato Motohashi.

At least 37 records · Page 2Linked to original sources

arXiv2026

Resonance in black hole ringdown: Benchmarking quasinormal mode excitation and extraction

We investigate how resonant excitation near exceptional points manifests in Kerr black hole ringdown waveforms and examine its extraction. Using waveforms generated by localized initial data, where quasinormal mode amplitudes are given solely by excitation factors, we establish a controlled benchmark for overtone extraction. Applying an iterative fitting method with mirror modes, we analyze a mild resonance in the $(l,m)=(2,2)$ multipole and a sharp resonance in the $(3,1)$ multipole occurring as part of a sequence of successive resonances. For $(2,2)$, we extract the fundamental mode, the first three overtones, and the fundamental mirror mode with relative errors below $10\%$, and show that residual waveforms exhibit the expected damped sinusoids together with distinctive resonance signatures. For $(3,1)$, we demonstrate that resonances can not only amplify but also reduce quasinormal mode excitations, reshaping the overtone hierarchy and rendering the sharp resonance more pronounced in ringdown. Our results clarify the imprint of resonance in Kerr ringdown and highlight both the robustness and limitations of current extraction techniques, providing a foundation for more reliable extraction of higher overtones and for applications to observational data analysis.

gr-qc↗

arXiv2025

Hybrid algorithm combining matched filtering and convolutional neural networks for searching gravitational waves from binary black hole mergers

Efficient searches for gravitational waves from compact binary coalescence are crucial for gravitational wave observations. We present a proof-of-concept for a method that utilizes a neural network taking an SNR map, a stack of SNR time series calculated by the matched filter, as input and predicting the presence or absence of gravitational waves in observational data. We demonstrate our algorithm by applying it to a dataset of gravitational-wave signals from stellar-mass black hole mergers injected into stationary Gaussian noise. Our algorithm exhibits comparable performance to the standard matched-filter pipeline and to the machine-learning algorithms that participated in the mock data challenge, MLGWSC-1. The demonstration also shows that our algorithm achieves reasonable sensitivity with practical computational resources.

gr-qc↗

arXiv2025

Resonance of black hole quasinormal modes in coupled systems

Black hole quasinormal modes (QNMs) can exhibit resonant excitations associated with avoided crossings in their complex frequency spectrum. Such resonance phenomena can serve as novel signatures for probing new physics, where additional degrees of freedom are commonly introduced. Motivated by this possibility, we investigate QNMs in systems where multiple degrees of freedom are coupled with each other, and introduce a definition of excitation factors suitable for such systems. To demonstrate our formulation, we apply it to a black hole in the Einstein-Maxwell-axion theory, where we find that avoided crossings can appear even between longest-lived modes originating from the fundamental modes of different degrees of freedom, in contrast to the Kerr case in General Relativity. We show that the excitation factors are indeed amplified as a manifestation of resonance at parameter values corresponding to the avoided crossings.

gr-qc↗

arXiv2025

Primordial black holes and induced gravitational waves from logarithmic non-Gaussianity

We investigate the formation of primordial black hole (PBH) based on numerical relativity simulations and peak theory as well as the corresponding scalar induced gravitational wave (SIGW) signals in the presence of \emph{logarithmic non-Gaussianities} which has recently been confirmed in a wide class of inflation models. Through numerical calculations, we find certain parameter spaces of the critical thresholds for the type A PBH formation and reveal a maximum critical threshold value. We also find that there is a region where no PBH is produced from type II fluctuations contrary to a previous study. We then confirm that SIGW signals originated from the logarithmic non-Gaussianity are detectable in the Laser Interferometer Space Antenna if PBHs account for whole dark matter. Finally, we discuss the SIGW interpretation of the nHz stochastic gravitational wave background reported by the recent pulsar timing array observations. We find that PBH overproduction is a serious problem for most of the parameter space, while this tension might still be alleviated in the non-perturbative regime.

astro-ph.CO↗

arXiv2025

Resonant Excitation of Quasinormal Modes of Black Holes

We elucidate that a distinctive resonant excitation between quasinormal modes (QNMs) of black holes emerges as a universal phenomenon at an avoided crossing near the exceptional point through high-precision numerical analysis and theory of QNMs based on the framework of non-Hermitian physics. This resonant phenomenon not only allows us to decipher a long-standing mystery concerning the peculiar behaviors of QNMs but also stands as a novel beacon for characterizing black hole spacetime geometry. Our findings pave the way for rigorous examinations of black holes and the exploration of new physics in gravity.

gr-qc↗

arXiv2025

Constant roll and non-Gaussian tail in light of logarithmic duality

The curvature perturbation in a model of constant-roll (CR) inflation is interpreted in view of the logarithmic duality discovered in Ref. [1] according to the $δN$ formalism. We confirm that the critical value $β:=\ddotφ/(H\dotφ)=-3/2$ determining whether the CR condition is stable or not is understood as the point at which the dual solutions, i.e., the attractor and non-attractor solutions of the field equation, are interchanged. For the attractor-solution domination, the curvature perturbation in the CR model is given by a simple logarithmic mapping of a Gaussian random field, which can realise both the exponential tail (i.e., the single exponential decay) and the Gumbel-distribution-like tail (i.e., the double exponential decay) of the probability density function, depending on the value of $β$. Such a tail behaviour is important for, e.g., the estimation of the primordial black hole abundance.

astro-ph.CO↗

arXiv2024

Spin wave optics for gravitational waves lensed by a Kerr black hole

Gravitational waves exhibit the unique signature of their spin-2 nature in processes of wave scattering, due to the interaction between spin and a background spacetime. Since the spin effect is more pronounced for longer wavelengths and gravitational waves sourced by binaries have a long wavelength, it may become an important effect in addition to the wave effect. We study the propagation of gravitational waves lensed by a Kerr black hole by numerically solving the Teukolsky equation with a source term of the equal-mass circular binary, taking into account both spin effect and wave effect. We find helicity-dependent small-period oscillation in the power spectrum of the amplification factor in the forward direction and the oscillation is enhanced as spin of a prograde Kerr black hole increases.

gr-qc↗

arXiv2024

Iterative extraction of overtones from black hole ringdown

Extraction of multiple quasinormal modes from ringdown gravitational waves emitted from a binary black hole coalescence is a touchstone to test whether a remnant black hole is described by the Kerr spacetime in general relativity. However, it is not straightforward to check the consistency between the ringdown signal and the quasinormal mode frequencies predicted by the linear perturbation theory. While the longest-lived mode can be extracted in a stable manner, the higher overtones damp more quickly and hence the fitting of overtones tends to end up with the overfit. To improve the extraction of overtones, we propose an iterative procedure consisting of fitting and subtraction of the longest-lived mode of the ringdown waveform in the time domain. Through the analyses of the mock waveform and numerical relativity waveform, we clarify that the iterative procedure allows us to extract the overtones in a more stable manner.

gr-qc↗

arXiv2024

Exact solution for rotating black holes in parity-violating gravity

It has recently been pointed out that one can construct invertible conformal transformations with a parity-violating conformal factor, which can be employed to generate a novel class of parity-violating ghost-free metric theories from general relativity. We obtain exact solutions for rotating black holes in such theories by performing the conformal transformation on the Kerr solution in general relativity, which we dub conformal Kerr solutions. We explore the geodesic motion of a test particle in the conformal Kerr spacetime. While null geodesics remain the same as those in the Kerr spacetime, timelike geodesics exhibit interesting differences due to an effective external force caused by the parity-violating conformal factor.

gr-qc↗

arXiv2023

Black hole ringdown from physically sensible initial value problem in higher-order scalar-tensor theories

We study odd-parity perturbations about static and spherically symmetric black hole solutions with a linearly time-dependent scalar field in higher-order scalar-tensor theories. In particular, we consider stealth Schwarzschild and stealth Schwarzschild-de Sitter solutions, where the deviation from the general relativity case is controlled by a single parameter. We find that complex frequencies of quasinormal modes (QNMs) are given by a simple scaling of those in general relativity. We also show that there is a degeneracy between the parameter characterizing the modification from general relativity and the black hole mass. We then consider a physically sensible initial value problem by taking into account the fact that the effective metric for the odd-parity perturbations is in general different from the background metric. We confirm that damped oscillations appearing at late times are indeed dominated by the QNMs. Our analysis includes the case where the perturbations are superluminal, and we demonstrate in this case that the perturbations can escape from the region inside the horizon for the background metric.

gr-qc↗

arXiv2023

Squeezed bispectrum and one-loop corrections in transient constant-roll inflation

In canonical single-field inflation, the production of primordial black holes (PBH) requires a transient violation of the slow-roll condition. The transient ultra slow-roll inflation is an example of such scenarios, and more generally, one can consider the transient constant-roll inflation. We investigate the squeezed bispectrum in the transient constant-roll inflation and find that Maldacena's consistency relation holds for a sufficiently long-wavelength mode, whereas it is violated for modes around the peak scale for the non-attractor case. We also demonstrate how the one-loop corrections are modified compared to the case of the transient ultra slow-roll inflation, focusing on representative one-loop terms originating from a time derivative of the second slow-roll parameter in the cubic action. We find that the perturbativity requirement on those terms does not rule out the production of PBH from the transient constant-roll inflation. Therefore, it is a simple counterexample of the recently claimed no-go theorem of PBH production from single-field inflation.

astro-ph.CO↗

arXiv2023

Consistency of matter coupling in modified gravity

Matter coupling in modified gravity theories is a nontrivial issue when the gravitational Lagrangian possesses a degeneracy structure to avoid the problem of the Ostrogradsky ghost. Recently, this issue was addressed for bosonic matter fields in the generalized disformal Horndeski class, which is so far the most general class of ghost-free scalar-tensor theories obtained by performing a higher-derivative generalization of invertible disformal transformations on Horndeski theories. In this paper, we clarify the consistency of fermionic matter coupling in the generalized disformal Horndeski theories. We develop the transformation law for the tetrad associated with the generalized disformal transformation to see how it affects the fermionic matter coupling. We find that the consistency of the fermionic matter coupling requires an additional condition on top of the one required for the bosonic case. As a result, we identify a subclass of the generalized disformal Horndeski class which allows for consistent coupling of ordinary matter fields, including the standard model particles.

gr-qc↗

arXiv2023

Quasinormal modes of Schwarzschild black holes on the real axis

We study the scattering of gravitational waves by a Schwarzschild black hole and its perturbed siblings to investigate influences of proposed spectral instability of quasinormal modes on the ringdown signal. Our results indicate that information of dominant ringdown signals, which are ascribed to the fundamental (i.e., least damping) quasinormal mode of unperturbed Schwarzschild black holes, is imprinted in the phase shift defined from the transmission amplitude (1/A_{in} in our notation). This approximately parallels the fact that the resonance of quantum systems is imprinted in the phase shift of the S-matrix. The phase shift around the oscillation frequency of the fundamental mode is modified only perturbatively even if the quasinormal-mode spectrum is destabilized by a perturbative bump at a distant location, signifying the stability of the ringdown signal. At the same time, the phase shift at low frequencies is modulated substantially reflecting the late-time excitation of echo signals associated with the quasinormal-mode spectrum after destabilization.

gr-qc↗

arXiv2023

Generalized disformal Horndeski theories: cosmological perturbations and consistent matter coupling

Invertible disformal transformations are a useful tool to investigate ghost-free scalar-tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel class of ghost-free scalar-tensor theories, which we dub generalized disformal Horndeski theories. Specifically, these theories lie beyond the quadratic/cubic DHOST class. We explore cosmological perturbations to identify a subclass where gravitational waves propagate at the speed of light and clarify the conditions for the absence of ghost/gradient instabilities for tensor and scalar perturbations. We also investigate the conditions under which a matter field can be consistently coupled to these theories without introducing unwanted extra degrees of freedom.

gr-qc↗

arXiv2022

Differentiation identities for hypergeometric functions

It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions have been used widely in various fields of applied mathematics and natural sciences. In this expository note, we provide a simple proof of the differentiation identities, which is based only on the definition of the coefficients for the power series expansion of the hypergeometric functions.

math.CA↗

arXiv2022

Physical effects of gravitational waves: pedagogical examples

General relativity describes gravitation in terms of the geometry of spacetime. It predicts the existence of gravitational waves (GWs) that stretch and compress spacetime and were detected recently by state-of-the-art interferometer observations. Yet, for those who are not familiar with general relativity, it may be difficult to understand how the GWs actually stretch and compress spacetime. In this paper, after reviewing the fact that the effects of GWs can be understood as a force in Newtonian mechanics, we consider extreme and readily perceivable situations where large-amplitude GWs pass through the human body and the Earth, and demonstrate that GWs cause phenomena that commonly occur in daily life by back-of-the-envelope calculations. Our analysis provides intellectual and pedagogical materials for understanding the nature of GWs for nonexperts in general relativity.

physics.pop-ph↗

arXiv2022

Spectroscopy of Kerr-AdS$_5$ spacetime with the Heun function: Quasinormal modes, greybody factor, and evaporation

We investigate quasinormal modes, greybody factor, and Hawking evaporation of a five-dimensional Kerr-anti de Sitter (AdS$_5$) black hole by solving a wave equation for a test massive scalar field in terms of the local Heun function. We clarify the distribution of the quasinormal modes satisfying the ingoing and decaying boundary conditions at the event horizon and conformal infinity, respectively, and their splitting behaviors in the complex frequency plane with respect to a variation of spin parameters. We also point out the existence of purely imaginary modes. Further, we develop a method to extract in/outgoing waves near the AdS boundary, which enables us to define the greybody factor for a wide range of parameter space complementary to previous works. Using the greybody factor, we compute evaporation rates for mass and spins for the Kerr-AdS$_5$ black hole via the Hawking radiation of the scalar field.

gr-qc↗

arXiv2022

Evaporation of Echoing Black Holes

We compute the graybody factor and evaporation rate of a rotating black hole in the presence of a hypothetical reflective surface slightly outside the outer horizon radius, assuming that it spontaneously emits thermal radiation due to quantum-gravitational effects such as firewalls or stretched horizons. As a result of a resonance caused by a cavity between the reflective surface and angular momentum barrier, the graybody factor is subject to a modulation in the frequency space. By taking into account this effect for multiangular modes of neutrinos, photons, and gravitons, we numerically compute the time development of the mass and angular momentum of the black hole, and show that the excited reflective surface shortens the lifetime of quantum black holes.

gr-qc↗