arXiv subjects

Shui-Fa Shen

Publications and source records attributed to Shui-Fa Shen.

9 recordsLinked to original sources

arXiv2026

On the instability of the fundamental mode of the Regge-Wheeler effective potential

It was recently pointed out that the fundamental mode of the Regge-Wheeler effective potential is unstable against an insignificant Gaussian metric perturbation, which, in turn, might substantially challenge the black hole spectroscopy. This intriguing result has been interpreted by some authors as arising from essentially replacing the black hole's effective potential and its perturbation with two disjoint potential barriers. We argue that such an analysis may have oversimplified the real physical scenario. To be more precise, a metric perturbation planted farther away from the black hole horizon might not always be appropriately approximated by a disjoint minor barrier. Particularly, for the perturbed P\"oschl-Teller potential, joint and disjoint metric perturbations might lead to drastically different stability properties for the low-lying modes. Following this line of thought, this study conducts a refined analysis of the stability of the fundamental mode of the Regge-Wheeler effective potential by closely examining a few physically relevant ingredients. While our analysis qualitatively confirms the main findings of previous studies, as the stability of the fundamental mode is primarily determined by the imaginary part of the quasinormal frequency, we show that specific features of both the effective potential at spatial infinity and the metric perturbation can have a sizable impact on the instability. In contrast, the spiral period, governed by the real part of the quasinormal frequency, appears largely insensitive to the details of the black hole metric or its perturbations. The analytic estimates are in reasonable agreement with the numerical results.

gr-qc↗

arXiv2025

Spectral instability in modified P\"oschl-Teller effective potential triggered by deterministic and random perturbations

Owing to its substantial implications for black hole spectroscopy, spectral instability has attracted considerable attention in the literature. While the emergence of such instability is attributed to the non-Hermitian nature of the gravitational system, it remains sensitive to various factors. About the spatial scale of the metric deformation, spectral instability is particularly susceptible to ``ultraviolet'' metric perturbations. In this work, we conduct a focused analysis of black hole spectral instability using the P\"oschl-Teller potential as a toy model. We investigate the dependence of the resulting spectral instability on the magnitude, spatial scale, and localization of deterministic and random perturbations in the effective potential of the wave equation, and discuss the underlying physical interpretations. It is observed that small perturbations in the potential initially have a limited impact on the less damped black hole quasinormal modes with deviations typically around their unperturbed values, a phenomenon first derived by Skakala and Visser in a more restrictive context. In the higher overtone region, the deviation propagates, amplifies, and eventually gives rise to spectral instability and, inclusively, bifurcation in the quasinormal mode spectrum. While deterministic perturbations give rise to a deformed but well-defined quasinormal spectrum, random perturbations lead to uncertainties in the resulting spectrum. Nonetheless, the primary trend of the spectral instability remains consistent, being sensitive to both the strength and location of the perturbation. However, we demonstrate that the observed spectral instability might be suppressed for perturbations that are physically appropriate.

gr-qc↗

arXiv2025

On Hyperboloidal Foliations in the Study of Black Hole Quasinormal Modes

In this work, we demonstrate that the hyperboloidal foliation technique, applied to the study of black hole quasinormal modes, where the spatial boundary is shifted from spacelike infinity to the future event horizon and null infinity, is effectively equivalent to the continued fraction approach, in which the asymptotic wave function typically diverges at both ends of spatial infinity. Specifically, a given hyperboloidal slicing, corresponding to a particular choice of coordinates, always uniquely determines a scheme for extracting the asymptotic form of the wave function at the spatial boundary. Owing to the mathematical equivalence, it follows that the efficiency and precision observed using the hyperboloidal approach should be attributed, not to avoiding the pathological behavior at the spatial boundaries, but primarily to other factors, such as the use of Chebyshev grids.

gr-qc↗

arXiv2025

Asymptotic quasinormal modes, echoes, and black hole spectral instability: a brief review

We present a short review of the analytical aspects of recent progress in the study of black hole spectral instability and its potential observational consequences. This topic, inspired by earlier foundational works, has attracted considerable attention in the recent literature. It has been demonstrated that both the low-lying modes and high overtones of black hole quasinormal spectra can be substantially influenced by small deformations in the effective potential of the wave equation that describes black hole perturbations. The temporal evolution of gravitational wave signals is primarily governed by the first few low-lying quasinormal modes. In contrast, the asymptotic behavior of high overtones is closely associated with the phenomenon of black hole echoes. We review relevant studies on spectral instability in both regimes, highlighting their potential to produce substantial observational signatures in gravitational wave data. Additionally, recent proposals of Regge poles and reflectionless modes as alternative stable observables for probing black hole spacetimes are summarized.

gr-qc↗

arXiv2025

An MLE analysis on the relationship between the initial-state granularity and final-state flow factorization

In this study, we employ the maximum likelihood estimator (MLE) to investigate the relationship between initial-state fluctuations and final-state anisotropies in relativistic heavy-ion collisions. The granularity of the initial state, reflecting fluctuations in the initial conditions (IC), is modeled using a peripheral tube model. Besides differential flow, our analysis focuses on a class of more sensitive observables known as flow factorization. Specifically, we evaluate these observables using MLE, an asymptotically normal and unbiased tool in standard statistical inference. Our findings show that the resulting differential flow remains essentially unchanged for different IC defined by the peripheral tube model. The resulting harmonic coefficients obtained using MLE and multi-particle cumulants are found to be consistent. However, the calculated flow factorizations show significant variations depending on both the IC and the estimators, which is attributed to their sensitivity to initial-state fluctuations. Thus, we argue that MLE offers a compelling alternative to standard methods such as multi-particle correlators, particularly for sensitive observables constructed from higher moments of the azimuthal distribution.

nucl-th↗

arXiv2024

Two distinct types of echoes in compact objects

In the black hole perturbation theory framework, two different physical pictures for echoes in compact objects have been proposed. The first mechanism interprets echoes as repeated reflections of gravitational waves within a potential well, where the echo period is defined by twice the distance related to the spatial displacement operator that separates two local maxima of the effective potential. The second mechanism associates echoes with a discontinuity in the effective potential, potentially associated with specific accretion processes, without necessarily introducing a second local maximum in the effective potential. This discontinuity leads to echo signals that are typically attenuated over time more quickly, with their period dictated by the characteristics of the transfer amplitudes. In both scenarios, the echoes correspond to a new category of quasinormal modes with minor real parts, with their period connected to the spacing between successive modes in the frequency domain. This work elaborates on a unified framework in compact stars that encompasses both echo mechanisms. It suggests that these two types of echoes derive from different physical origins and can be independently triggered. The occurrence and interplay between these two types of echoes are demonstrated through numerical simulations. %The observational relevance of this study is also addressed.

gr-qc↗

arXiv2024

Matrix method and the suppression of Runge's phenomenon

Higher-degree polynomial interpolations carried out on uniformly distributed nodes are often plagued by {\it overfitting}, known as Runge's phenomenon. This work investigates Runge's phenomenon and its suppression in various versions of the matrix method for black hole quasinormal modes. It is shown that an appropriate choice of boundary conditions gives rise to desirable suppression of oscillations associated with the increasing Lebesgue constant. For the case of discontinuous effective potentials, where the application of the above boundary condition is not feasible, the recently proposed scheme with delimited expansion domain also leads to satisfactory results. The onset of Runge's phenomenon and its effective suppression are demonstrated by evaluating the relevant waveforms. Furthermore, we argue that both scenarios are either closely related to or practical imitations of the Chebyshev grid. The implications of the present study are also addressed.

gr-qc↗

arXiv2022

An implementation of the matrix method using Chebyshev grid

In this work, we explore the properties of the matrix method for black hole quasinormal modes on the nonuniform grid. In particular, the method is implemented to be adapted to the Chebyshev grid, aimed at effectively suppressing Runge's phenomenon. It is found that while such an implementation is favorable from a mathematical point of view, in practice, the increase in precision does not necessarily compensate for the penalty in computational time. On the other hand, the original matrix method, though subject to Runge's phenomenon, is shown to be reasonably robust and suffices for most applications with a moderate grid number. In terms of computational time and obtained significant figures, we carried out an analysis regarding the trade-off between the two aspects. The implications of the present study are also addressed.

gr-qc↗

arXiv2022

Matrix method for perturbed black hole metric with discontinuity

Recent studies based on the notion of black hole pseudospectrum indicated substantial instability of the fundamental and high-overtone quasinormal modes. Besides its theoretical novelty, the details about the migration of the quasinormal mode spectrum due to specific perturbations may furnish valuable information on the properties of associated gravitational waves in a more realistic context. This work generalizes the matrix method for black hole quasinormal modes to cope with a specific class of perturbations to the metric featured by discontinuity, which is known to be intimately connected with the quasinormal mode structural instability. In practice, the presence of discontinuity poses a difficulty so that many well-known approaches for quasinormal modes cannot be straightforwardly applied. By comparing with other methods, we show that the modified matrix method is efficient, which can be used to solve for the low-lying modes with reasonable precision. Therefore, it might serve as an alternative gadget for relevant studies.

gr-qc↗