arXiv subjects

Hayato Motohashi

Publications and source records attributed to Hayato Motohashi.

At least 19 recordsLinked to original sources

arXiv2026

Exact Cancellation of Horizon Modes in Kerr Ringdown

Ringdown gravitational waves probe black hole spacetimes via quasinormal modes (QNMs). Recent studies have reported oscillatory features in QNM-filtered waveforms, and have led to conflicting interpretations as to whether they represent a near-horizon "direct wave". Reexamining a particle plunging into a Kerr black hole, we show that the saddle-point approximation underlying the proposed interpretation fails near the horizon. Our exact analysis reveals that every source-induced horizon-mode pole is canceled by an infinite tower of Matsubara zeros, independently of orbital and black-hole parameters. The first four stages of this sequential screening are also confirmed by time-domain numerical integration. Thus, within the near-horizon perturbative framework, source-induced horizon-mode signals do not survive at late times.

gr-qc↗

arXiv2026

Constant-Roll Inflation: Analytical Formulae for Power Spectrum and Implications for Induced Gravitational Waves

Constant-roll inflation provides a simple and analytically tractable framework for describing transient departures from slow roll, including non-attractor phases that can enhance the primordial curvature perturbation on small scales. In this work, we investigate the curvature power spectrum generated in a slow-roll--constant-roll--slow-roll scenario, focusing on the positions and amplitudes of the two characteristic peaks associated with the two transitions. We show that, in the parameter range where both peaks are well separated and sufficiently pronounced, the underlying constant-roll parameters can be reconstructed from the peak positions and amplitudes without performing a brute-force parameter scan. In addition, we construct a smoothed analytic approximation to the power spectrum, designed for efficient estimates of scalar-induced gravitational waves and related phenomenological applications.

astro-ph.CO↗

arXiv2026

Pole Skipping, Avoided Crossing, and Resonant Excitation in Kerr Quasinormal Modes near Algebraically Special Frequencies

Kerr quasinormal modes near algebraically special frequencies exhibit anomalous behavior, including apparent bifurcation, disappearance, and a nonsmooth connection to the Schwarzschild limit, which has remained puzzling for decades. Tracking poles and zeros of Green-function building blocks across different Riemann sheets, we show that the bifurcation is due to an avoided crossing accompanied by resonant excitation, while the disappearance is due to pole skipping caused by cancellation of a quasinormal-mode pole by a Matsubara-mode zero. This resolves the physical origin of these long-standing anomalies.

gr-qc↗

arXiv2026

Ringdown analysis of GW250114 with orthonormal modes

GW250114 is the loudest gravitational wave event to date observed by LIGO-Virgo-KAGRA Collaboration. Owing to its high signal-to-noise ratio (SNR), previous analyses based on quasinormal mode (QNM) superpositions have suggested evidence of the fundamental and the first overtone of the $\ell=m=2$ mode in this event. However, QNMs are not orthogonal and the inclusion of multiple QNMs induces correlations among them, which can hinder the robust identification of subdominant QNMs. To address this challenge, we apply an analysis based on orthonormalized QNMs [S. Morisaki $\textit{et al.}$, Phys. Rev. D $\textbf{112}$, 124083 (2025)] to GW250114. We find that, in the model including three $\ell=m=2$ QNMs up to the second overtone, the first overtone of the $\ell=m=2$ mode is more strongly supported than in previous nonorthogonal analyses, with the inferred significance increasing from $82.5\%$ to $99.9\%$. Furthermore, we estimate deviations from the Kerr prediction using the orthonormal QNM framework and find no significant deviation, consistent with previous analyses. These results demonstrate that the orthonormal QNM framework provides a more robust way to identify subdominant modes in high-SNR ringdown signals, highlighting its potential for future gravitational wave observations.

gr-qc↗

arXiv2026

Pole structure of the Kerr Green's function

We investigate the pole structure of Kerr black-hole perturbations in the frequency domain, focusing on the building blocks of the Green's function for the radial Teukolsky equation: the homogeneous radial solutions, the connection coefficients, and the Green's function itself. We show that the homogeneous solutions and the local connection coefficients develop simple poles at the Matsubara frequencies, thereby establishing the Matsubara pole structure explicitly within the Teukolsky formalism for asymptotically flat Kerr black holes. At the level of the local fixed-sector connection formula, the explicit Matsubara-pole factors cancel in the ratio of connection coefficients entering a decomposed Green's function contribution. We also identify higher-order zero-frequency singularities in the decomposed Green's function contributions, which scale as $\omega^{-2l-1}$ and cancel collectively in the total radial Green's function. These results clarify how Matsubara poles and sectoral zero-frequency singularities arise in the Teukolsky formalism and provide a frequency-domain foundation for understanding prompt response in time-domain ringdown waveforms in Kerr spacetime.

gr-qc↗

arXiv2026

Autoencoder-Based Parameter Estimation for Superposed Multi-Component Damped Sinusoidal Signals

Damped sinusoidal oscillations are widely observed in many physical systems, and their analysis provides access to underlying physical properties. However, parameter estimation becomes difficult when the signal decays rapidly, multiple components are superposed, and observational noise is present. In this study, we develop an autoencoder-based method that uses the latent space to estimate the frequency, phase, decay time, and amplitude of each component in noisy multi-component damped sinusoidal signals. We investigate multi-component cases under Gaussian-distribution training and further examine the effect of the training-data distribution through comparisons between Gaussian and uniform training. The performance is evaluated through waveform reconstruction and parameter-estimation accuracy. We find that the proposed method can estimate the parameters with high accuracy even in challenging setups, such as those involving a subdominant component or nearly opposite-phase components, while remaining reasonably robust when the training distribution is less informative. This demonstrates its potential as a tool for analyzing short-duration, noisy signals.

cs.LG↗

arXiv2026

Scalar quasinormal modes of rotating black holes in parity-violating gravity

Recently, an exact rotating black hole solution in a parity-violating theory of gravity was obtained via a conformal transformation of the Kerr solution in general relativity, with parity-violating effects encoded in the conformal factor. We study the quasinormal modes (QNMs) of a test scalar field minimally coupled to gravity on this conformal Kerr background, treating the parity-violating effects perturbatively while allowing for arbitrary black hole spin, from the non-rotating case to the near-extremal regime. For low spin, we derive a perturbative formula for the QNM frequencies that includes the leading-order parity-violating correction. For high spin, particularly in the near-extremal regime, we find sizable deviations from the Kerr QNM frequencies. Our results point to a new avenue for probing parity-violating physics in the strong-gravity regime through black hole QNMs.

gr-qc↗

arXiv2025

Probing higher curvature gravity via ringdown with overtones

We investigate metric perturbations of a spherically symmetric black hole in higher curvature gravity. We show that higher curvature corrections deform the near-horizon region of the effective potential, and that the deviations of the quasinormal mode (QNM) frequencies from their general relativity (GR) values become more pronounced for overtone modes. We find that, as the order of the higher curvature term increases, the deformations approach the horizon and the deviations of the overtone QNM frequencies grow progressively larger. We also analyze the ringdown waveforms in the higher curvature gravity model. We consider setups in which the deviations from the vacuum-GR QNMs remain mild for the fundamental mode and the first few overtones, and show that these shifted QNMs can be identified in the ringdown signal through waveform fitting.

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

Exceptional Points and Resonance in Black Hole Ringdown

We propose an exceptional-point (EP) framework for black-hole ringdown beyond the standard quasinormal-mode (QNM) paradigm. It provides a first-principles characterization of the resonance associated with avoided crossings near EPs, an effect that conventional QNM analysis cannot fully capture. Employing a phenomenological environmental black-hole model with the hyperboloidal framework, we identify near-coalescence of both QNM eigenvalues and eigenfunctions, and directly demonstrate that the resonance produces enhanced mode contributions in the time domain, resulting in characteristic departures from exponentially damped oscillations. Our formulation further reveals that the EP frequency, given by the average of the resonant modes, emerges as the physically relevant observable in the near-EP regime, and offers a robust foundation for modeling and extracting resonant ringdown signals.

gr-qc↗

arXiv2025

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

Analyzing black-hole ringdowns with orthonormal modes

The ringdown signal following a black hole (BH) merger can be modeled as a superposition of BH quasinormal modes (QNMs), offering a clean setup for testing gravitational theories. In particular, detecting multiple QNMs enables consistency checks of their frequencies and damping times, serving as a test of general relativity -- a technique known as black hole spectroscopy. However, incorporating additional QNMs introduces challenges such as increased parameter correlations and higher computational costs in data analysis. To address this, we propose an efficient Bayesian analysis method that applies the Gram-Schmidt algorithm to the QNMs. This reduces the correlation between the modes and enables analytic marginalization over the mode amplitudes. We validate our approach using damped sinusoids and numerical waveforms from the Simulating eXtreme Spacetimes catalog.

gr-qc↗

arXiv2025

Black hole spectroscopy: from theory to experiment

The "ringdown" radiation emitted by oscillating black holes has great scientific potential. By carefully predicting the frequencies and amplitudes of black hole quasinormal modes and comparing them with gravitational-wave data from compact binary mergers we can advance our understanding of the two-body problem in general relativity, verify the predictions of the theory in the regime of strong and dynamical gravitational fields, and search for physics beyond the Standard Model or new gravitational degrees of freedom. We summarize the state of the art in our understanding of black hole quasinormal modes in general relativity and modified gravity, their excitation, and the modeling of ringdown waveforms. We also review the status of LIGO-Virgo-KAGRA ringdown observations, data analysis techniques, and the bright prospects of the field in the era of LISA and next-generation ground-based gravitational-wave detectors.

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

Constant-Roll Inflation

Constant-roll inflation is a distinctive class of phenomenological inflationary models in which the inflaton's rate of roll remains constant. It provides an exact solution that is compatible with the latest observational constraints and offers a natural framework for enhancing the curvature power spectrum, which is relevant to the formation of primordial black holes. In this paper, I review constant-roll inflation in memory of Alexei Starobinsky.

astro-ph.CO↗

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↗