arXiv subjects

Wei-Liang Qian

Publications and source records attributed to Wei-Liang Qian.

At least 37 records · Page 2Linked to original sources

arXiv2025

Spectral instability in modified Pöschl-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 Pöschl-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 angular dependent response to gravitational-wave signals for time-delay interferometry combinations

Space-based gravitational wave (GW) detectors are designed for wave sources in the millihertz band with different locations and orientations. Time-delay interferometry (TDI) technique is an indispensable ingredient in space-borne GW detection that effectively suppresses the laser phase noise. The abundant TDI solutions derived in the literature also feature distinct angular-dependent sensitivities. Because a GW source's angular location is unknown prior to the signals' detection, a solid-angle average is often performed when analyzing the sensitivity function of a given TDI combination. The present study explores the angular dependence of the detector's sensitivity. This detail is relevant, because once the initial detection is achieved, the source's location can be extracted and used to provide information on a refined TDI combination tailored for the specific GW source. As the TDI technique is a post-processing algorithm, such a procedure can be implemented in practice. We evaluate the angular dependence of the detector's response function to the GW signals for different TDI combinations as a function of the orientation angles. Moreover, we classify the response functions into seven categories at the low-frequency limit, leveraging the characteristics of the underlying geometrical TDI combinations. By further averaging out the azimuthal angle $ϕ_D$ in the detector's plane, the main features of the resulting response functions and their zenithal dependence with respect to the GW source are scrutinized. The findings presented in this work provide pertinent insights for ongoing space-borne detector programs.

gr-qc↗

arXiv2025

Cosmological Model Independent Constraints on Lorentz Invariance Violation with Updated Gamma-Ray Burst Observations: An Artificial Neural Network Approach

Searching for Lorentz invariance violation (LIV) using astrophysical sources such as gamma-ray bursts (GRBs) is crucial for probing quantum gravity. However, the dependence of LIV constraints on assumed cosmological models has been largely overlooked. In this work, we present a model-independent reconstruction of the cosmic expansion history using artificial neural networks (ANN), thereby avoiding biases from specific cosmological priors. We analyze 74 GRB time delays, including 37 measurements from GRB~160625B across multiple energy bands at $z = 1.41$, and 37 additional bursts spanning redshifts $0.117 \leq z \leq 1.99$. Our analysis yields stringent constraints on both linear and quadratic LIV, with $E_{\mathrm{QG},1} \geq 2.60 \times 10^{15}~\mathrm{GeV}$ and $E_{\mathrm{QG},2} \geq 1.21 \times 10^{10}~\mathrm{GeV}$. The linear limit is within four orders of magnitude of the Planck scale. By leveraging a large sample of GRBs, our approach significantly enhances the robustness of LIV constraints, providing a powerful, cosmological-independent framework for future tests of quantum gravity.

astro-ph.HE↗

arXiv2025

Novel black holes with scalar hair in the Einstein-Maxwell-Scalar Theory with positive coupling

In this work, we find a new branch of hairy black hole solutions in the Einstein-Maxwell-Scalar (EMS) theory in four-dimensional asymptotically flat spacetimes. Different from spontaneous scalarization induced by tachyonic instabilities in Reissner-Nordström (RN) black holes with a negative coupling parameter, these scalar-hairy black hole solutions arise when the coupling parameter is positive, where nonlinear coupling plays the dominant role, meaning that the coupling is positively correlated with the degree of deviation from the trivial state. Our numerical analysis reveals that the scalar field grows monotonically with the radial coordinate and asymptotically approaches a finite constant, exhibiting behavior that is qualitatively similar to that of the Maxwell potential. In these solutions, an increase in the charge $q$ causes the scalar-hairy solutions to deviate further from the RN state, while excessive charging drives the system back towards hairless solutions. Strengthening the coupling parameter compresses the existence domain of the scalar-hairy state, which lies entirely within the parameter region of RN black holes. Moreover, by evaluating the quasinormal modes, we show that the obtained scalar-hairy solutions are stable against linearized scalar perturbations.

gr-qc↗

arXiv2025

A Critical Point on the Hairy Black Hole Phase Boundary in the Improved Holographic Einstein-Maxwell-Dilaton Theory

In this work, we investigate the hairy black hole solutions and their dual phase diagram in the improved holographic Einstein-Maxwell-Dilaton (EMD) model.From the gravitational perspective, the rich phase structures observed in the dual boundary field theory originate from the intricate interplay between the scalar field formalism and the Maxwell field coupling mechanism. Two distinct types of hairy black hole solutions are found in this framework. Type-I hairy black holes are predominantly governed by scalar potential dynamics, whereas Type-II solutions emerge through nonminimal coupling to the $U(1)$ gauge field. We map out the phase distribution in the $(μ_B,T)$ parameter plane and delineate the boundary separating these two hairy phases. The phase diagram exhibits a first-order phase transition line consistent with previous findings, accompanied by a subtle third-order phase transition line that terminates at a critical point positioned at the turning point of the entire phase boundary curve. Our results complement existing research on holographic EMD theory by offering a comprehensive characterization of phase distributions, transition boundaries, and their gravitational sector interpretations. These insights will enable more effective engineering of specific phase structures for simulating strongly coupled systems through targeted modifications to the EMD model.

hep-th↗

arXiv2025

Regge poles, grey body factors, and absorption cross sections for black hole metrics with discontinuity

It was recently proposed by Rosato {\it et al.} and Oshita {\it et al.} that black hole greybody factors, as stable observables at relatively high frequencies, are more relevant quantities than quasinormal modes in modeling ringdown spectral amplitudes. It was argued that the overall contributions of spectrally unstable quasinormal modes conspire to produce stable observables through collective interference effects. In this regard, the present study investigates the Regge poles, the underlying quantities of the greybody factor governed by the singularities in the complex angular momentum plane, for perturbed black hole metrics. To this end, we generalize the matrix method to evaluate the Regge poles in black hole metrics with discontinuities. To verify our approach, the numerical results are compared with those obtained using a modified version of the continued fraction method. The obtained Regge pole spectrum is then used to calculate the scattering amplitude and cross-section. We show that the stability of these observables at moderate frequencies can be readily interpreted in terms of the stability of the Regge pole spectrum, particularly the low-lying modes. Nonetheless, destabilization still occurs at higher frequencies, characterized by the emergence of a bifurcation in the spectrum. The latter further evolves, leading to more significant deformation in the Regge poles, triggered by ultraviolet metric perturbations moving further away from the black hole. However, based on the validity of the WKB approximation, it is argued that such an instability in the spectrum is not expected to cause significant observable implications.

gr-qc↗

arXiv2025

Echoes of bimodal axial gravitational perturbations in a uniform-density star in Einstein-Æther gravity

This paper studies axial gravitational perturbations of a uniform-density star in scalar-Einstein-Æther theory. By applying the Israel junction conditions explicitly in the presence of a scalar field minimally coupled to the gravitational sector, it is shown that a nontrivial scalar profile cannot be sustained, as it induces a divergence at the stellar center. Since analytical solutions are unattainable, the background metric is determined through numerical integration for a few representative configurations. For axial gravitational perturbations, it is found that the system of equations of motion cannot be decoupled as long as the Æther parameter $c_i$ does not vanish. Subsequently, the dynamics of the system can be simplified to two coupled equations that describe vector and tensor perturbations with distinct wave velocities $c_V$ and $c_T$, giving rise to a bimodal system. It is shown that as the stellar radius is smaller than that of the maximum of the vacuum Schwarzschild-type effective potential, a potential well is formed, leading to the emergence of echo phenomenon for the axial gravitational perturbations. When the stellar radius exceeds the {\it could-have-been} maximum, the resulting effective potential decreases monotonically, and the wave propagation is primarily dictated by the discontinuity occurring at the star's surface, producing a type of more attenuated echo waves. In addition, we explore the specific properties of the resultant bimodal medium consisting of two degrees of freedom with distinct sound speeds. However, it is understood that such a characteristic does not lead to observational implications, and subsequently hardly offers a potential empirical means to constrain specific metric parameters of the Einstein-Æther. We present numerical calculations and discuss the potential implications of our findings.

gr-qc↗

arXiv2025

Capacity drop induced by stability modifications in stochastic dynamic systems

It is well-known that the fundamental diagram in a realistic traffic system is featured by capacity drop. From a mesoscopic approach, we demonstrate that such a phenomenon is linked to the unique properties of stochastic noise, which, when considered a specific perturbation, may counterintuitively enhance the stability of the originally deterministic system. We argue that the system achieves its asymptotic behavior through a trade-off between the relaxation towards the stable attractors of the underlying deterministic system and the stochastic perturbations that non-trivially affect such a process. Utilizing Itô calculus, the present study analyzes the threshold of the relevant perturbations that appropriately give rise to such a physical picture. In particular, we devise a scenario for which the stochastic noise is introduced in a minimized fashion to a deterministic fold model, which is known to reproduce the main feature of the fundamental diagram successfully. Our results show that the sudden increase in vehicle flow variance and the onset of capacity drop are intrinsically triggered by stochastic noise. Somewhat counterintuitively, we point out that the prolongation of the free flow state's asymptotic stability that forms the inverse lambda shape in the fundamental diagram can also be attributed to the random process, which typically destabilizes the underlying system. The asymptotic behaviors of the system are examined, corroborating well with the main features observed in the experimental data. The implications of the present findings are also addressed.

stat.AP↗

arXiv2025

Analysis of flow factorization and event-plane correlations based on a maximum likelihood estimator

In this study, we use the maximum likelihood estimator (MLE) to explore factorization and event-plane correlations in relativistic heavy-ion collisions. Our analyses incorporate both numerical simulations and publicly available data from the CMS Collaboration. We focus on Au+Au collisions at 200 GeV and Pb+Pb collisions at 2.76 TeV. The differential flows obtained for various centrality windows and momentum cuts are consistent with conventional methodologies such as multi-particle cumulants and event-plane methods. Leveraging these findings, we proceed to undertake further analysis of flow factorization and event-plane correlations. These quantities are relevant because of their sensitivity to initial-state fluctuations. While higher-order correlators might provide different implementations of factorization ratio, the MLE estimator is readily applied to these scenarios. Moreover, MLE's unique capabilities allow us to compute specific correlators that are typically inaccessible by other means. As an asymptotically normal and unbiased estimator, MLE provides a valuable alternative tool for flow and correlation analysis.

nucl-th↗

arXiv2025

The underlying black hole phase transitions in an Einstein-Maxwell-dilaton model with a holographic critical point

The Einstein-Maxwell-dilaton model exhibits a first-order phase transition curve that terminates at a holographic critical endpoint, offering intriguing insights into the phase diagram of the dual system living on the boundary. However, the specific instability within the underlying spacetime that triggers the formation of the hairy black hole remains somewhat obscure. This raises the question of whether one of the hairy black hole phases represents a superconducting or scalarized state and how the two distinct phases merge into a indistinguishable one at the critical point. This work investigates the associated black hole phase transition and the underlying instabilities by exploring a specific Einstein-Maxwell-dilaton model. The approach aims to provide transparent insights into the black hole phase transitions in the bulk. By introducing a nonminimal coupling between a massive real scalar field and a Maxwell field in a five-dimensional anti-de Sitter spacetime, we identify two types of scalarization corresponding to tachyonic instabilities in the ultraviolet and infrared regions. These distinct instabilities lead to a first-order phase transition between two phases in the $μ-T$ phase diagram. Furthermore, this first-order transition terminates at a critical point, beyond which the curve turns back, and the transition becomes a numerically elusive third-order one. Although one does not encounter a critical endpoint, the model still offers a consistent interpretation for the observed {\it cross-over} in the low baryon density region. We analyze the thermodynamic properties of the scalarized hairy black holes and discuss the implications of our findings.

hep-th↗

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↗

arXiv2025

Evolution of black hole echo modes and the causality dilemma

It has been shown that black hole quasinormal modes are subject to spectral instability, typically triggered by metric perturbations. These perturbations, which can introduce a minor bump in the effective potential of the wave equation, give rise to a novel branch of asymptotic quasinormal modes, dubbed the {\it echo modes}, which lie mainly parallel to the real frequency axis. This study explores the evolution of the echo modes and their interplay with the outward spiral motion observed in low-lying quasinormal modes. As the bump in the effective potential moves away from the central black hole, the echo modes collectively shift toward the real axis, with the spacing between successive modes decreasing uniformly. This collective motion occurs simultaneously with the spiral of the low-lying modes until the echo modes eventually take over the fundamental quasinormal mode. In the time domain, such a takeover coincides with a transition point for the temporal waveform, where the distinction between the original black hole's ringdown and the echoes becomes clear. This marks a transition in the characteristics of the waveform from primarily damped oscillations, dominated by the damping rate of the fundamental mode, to echo waves, characterized by periodic echo pulses. We argue that this phenomenon is universal by employing analytical and numerical analyses. We first elucidate our arguments using explicit but simplified toy models, where the effective potential barriers are disjoint. The derivations are then generalized to scenarios where perturbations are introduced on top of a black hole metric with a continuous effective potential. The observational implications, particularly the causality dilemma, are elaborated. We show that the echo modes can be extracted by applying the Fourier transform to ringdown waveforms, which can be important for gravitational wave observations.

gr-qc↗

arXiv2024

On the universality of instability in the fundamental quasinormal modes of black holes

We elaborate on a criterion for the emergence of instability in the fundamental mode recently observed by Cheung {\it et al.}, as a universal phenomenon in the context of black hole perturbations. Such instability is characterized by an exponential spiral, deviating from the quasinormal frequencies due to an insignificant perturbation moving away from the compact object. Our analysis begins with a specific case involving a truncated Pöschl-Teller potential for which we derive an explicit form of the criterion. Notably, it is shown analytically, contrary to other cases studied in the literature, that the fundamental mode is stable. These derivations are then generalized to a broader context, embracing two underlying mathematical formalisms. Specifically, the spiral is attributed to either the poles in the black hole's reflection amplitude or the zeros in the transmission amplitude. Additionally, we revisit and then generalize a toy model in which perturbations to the effective potential are disjointed, demonstrating that such a configuration invariably leads to instability in the fundamental mode, and the resulting outward spiral always occurs in the counter-clockwise direction. The derived criterion is not restricted to the fundamental mode but is generally relevant for the first few low-lying modes. We demonstrate numerically that the sprial's period and the frequency's relative deviation agree well with our analytical estimations.

gr-qc↗

arXiv2024

On sensitivity of nucleus deformation on final-state flow harmonics

In this work, we explore the effect of deformation of the nuclei on collective flow in relativistic heavy-ion collisions. The parameter associated with the geometrical deformation in the Glauber model is tuned to reproduce the empirical multiplicity probability distributions correctly. Subsequently, the particle spectra and collective flows for Au+Au and U+U collisions are evaluated using a hybrid hydrodynamic code CHESS. We analyze the effects of the degrees of freedom associated with the IC on the final-state flow harmonics by exploring the parameter space of the former. The connection between the deformation parameters, specifically $β_2$ and $β_4$, and the flow anisotropies is scrutinized. In particular, deviations in elliptic flow at $p_{\mathrm{T}}\sim 2$ GeV are observed at smaller values of $β_2$ in Au+Au collisions. On the other hand, for U+U collisions, the averaged overall flow harmonics are found to be less sensitive to the geometrical parameters. Despite the difference in the model's specifications, our findings largely confirm those obtained in the literature employing different approaches, which indicate that flow harmonics can be used as a sensible probe for the initial geometry fluctuations and to discriminate between different theoretical models.

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

Rapid Parameter Estimation for Extreme Mass Ratio Inspirals Using Machine Learning

Extreme-mass-ratio inspiral (EMRI) signals pose significant challenges in gravitational wave (GW) astronomy owing to their low-frequency nature and highly complex waveforms, which occupy a high-dimensional parameter space with numerous variables. Given their extended inspiral timescales and low signal-to-noise ratios, EMRI signals warrant prolonged observation periods. Parameter estimation becomes particularly challenging due to non-local parameter degeneracies, arising from multiple local maxima, as well as flat regions and ridges inherent in the likelihood function. These factors lead to exceptionally high time complexity for parameter analysis while employing traditional matched filtering and random sampling methods. To address these challenges, the present study applies machine learning to Bayesian posterior estimation of EMRI signals, leveraging the recently developed flow matching technique based on ODE neural networks. Our approach demonstrates computational efficiency several orders of magnitude faster than the traditional Markov Chain Monte Carlo (MCMC) methods, while preserving the unbiasedness of parameter estimation. We show that machine learning technology has the potential to efficiently handle the vast parameter space, involving up to seventeen parameters, associated with EMRI signals. Furthermore, to our knowledge, this is the first instance of applying machine learning, specifically the Continuous Normalizing Flows (CNFs), to EMRI signal analysis. Our findings highlight the promising potential of machine learning in EMRI waveform analysis, offering new perspectives for the advancement of space-based GW detection and GW astronomy.

physics.comp-ph↗

arXiv2024

Gravitational waves from extreme mass ratio inspirals in Kerr-MOG spacetimes

This work elaborates on a detailed analysis of the novel characteristics of gravitational waves (GWs) generated by extreme mass ratio inspirals (EMRIs) within the framework of modified gravity (MOG). Our study begins by exploring the geometrical and dynamical properties of the Kerr-MOG spacetime. We employ the numerical kludge (NK) method for waveform simulations and reveal that the parameter $α$, representing deviations from general relativity (GR), significantly impacts the frequencies of geodesic orbits and, consequently, the EMRI waveforms. However, the waveform confusion problem remains mainly unresolved, posing a challenge in distinguishing between the underlying gravitational theories based on the observed EMRI waveforms. Notably, by incorporating the effects of radiation reaction, we observe a substantial reduction in the waveform overlap over time. This reduction could enhance our ability to discern between different waveforms over an extended period.

gr-qc↗

arXiv2024

Late-time tail and echoes of Damour-Solodukhin wormholes

Damour-Solodukhin wormholes are intriguing theoretical constructs, closely mimicking many properties of black holes. This study delves into two distinct characteristics of the waveforms emitted from such wormholes, namely, the late-time tails and echoes, which can substantially be used to distinguish its identity. Notably, both features appear in the latter stages of quasinormal oscillations and stem from the singularities of the Green's function. The late-time tail, on the one hand, arises due to the branch cuts in the relevant Green's function. Within the Damour-Solodukhin wormhole paradigm, singularities are present in both ingoing and outgoing waveforms, which entails a generalization of the existing recipe for black hole metrics. On the other hand, the echoes are attributed to a new set of quasinormal poles, supplementing those of the respective black holes, reminiscent of the scenario where the spacetime metric possesses a discontinuity. It is inferred that both features are observationally relevant in distinguishing a wormhole from its black hole counterpart. Moreover, we suggest a potential interplay concerning the late-time evolution between the two mechanisms in question.

gr-qc↗