arXiv subjects

Ramin G. Daghigh

Publications and source records attributed to Ramin G. Daghigh.

At least 19 recordsLinked to original sources

arXiv2026

Effect of dark matter on galactic black hole ringdown waveforms and shadows

We calculate the effect of dark matter on the ringdown waveform and shadow of supermassive black holes at the core of galaxies. Our main focus is on the supermassive black hole at the core of M87, which is large enough to allow for viable observational data. We compare the effects of a dark matter spike to those expected from a galactic halo of the same mass. Our calculation for the halo starts from the Hernquist density function and assumes anisotropic pressure that is zero in the radial direction. The resulting Tolman-Oppenheimer-Volkoff equations allow the corresponding metric to be obtained analytically in closed form. The geometry of the anisotropic dark matter spike is the same as that obtained in [{\it ApJ} {\bf 940} 33 (2022)] under the assumption of isotropy. The effect of the spike is orders of magnitude more significant than the halo as long as the distribution scale of the latter is within a few orders of magnitude of the value expected from observations. Our results indicate that the impact of the spike surrounding M87* on the ringdown waveform may in principle be detectable. Finally, we point out the somewhat surprising fact that existing Event Horizon Telescope observations of black hole shadows are within an order of magnitude from being able to detect, or rule out, the presence of a spike.

gr-qc↗

arXiv2026

Sensitivity of black hole spectral instability to ultraviolet perturbations

Black hole quasinormal modes are known to exhibit spectral instability under ultraviolet perturbations of the effective potential. In the present work, we investigate the sensitivity of the fundamental mode to different types of localized perturbations through a combination of analytic and numerical analyzes. We show that the instability is governed primarily by the effective size of the perturbation rather than by its specific shape. In particular, the instability may persist even in the limit where the width of the perturbation vanishes, provided that the integrated strength of the perturbation is not zero. While a delta-function perturbation destabilizes the fundamental mode through an outward spiral, its interplay with a jump-discontinuity-type perturbation gives rise to competing inward and outward spiral motions. We further show that the stability of the fundamental mode depends sensitively on how the magnitude of the perturbation decreases as it moves away from the compact object, leading to qualitatively distinct outward spirals, inward spirals, and rotational trajectories. Finally, we investigate the motion of the fundamental mode in perturbed Regge-Wheeler potentials containing a jump discontinuity associated with a thin matter shell surrounding the black hole. The resulting behavior qualitatively resembles the spiral structure observed in double-sided Pöschl-Teller potentials, suggesting that the mechanisms identified in analytically tractable models persist in more realistic black hole effective potentials. The present results indicate that the spectral instability of low-lying black hole modes is considerably richer than previously anticipated and may have important implications for black hole spectroscopy in realistic astrophysical environments.

gr-qc↗

arXiv2026

Scalar Field Model for Dark Matter Spikes Surrounding Sgr A$^$ and M87$^$

Theoretical models suggest that the adiabatic growth of a black hole immersed in dark matter can lead to the formation of high density regions of dark matter, known as ``spikes'', near the black hole event horizon. The density of these spikes is determined theoretically and observationally to be a power law of the form $ρ(r) \propto r^{-γ_\text{sp}}$. It has been shown that the spike can potentially have a detectable impact on the emitted gravitational waves and shadow radius of the central black hole. In this work, we model the dark matter spike using a real scalar field with a non-standard potential. More specifically we ``reverse engineer'' the equations of motion to find a potential for the scalar field that permits a solution to the equations of motion with desired energy density and reasonable background geometry. We show that the emerging geometry is testable. In addition, the fact that the solution is derived from a covariant action makes it possible to study gravitational perturbations of the black hole in the presence of a spike including the backreaction of the spike.

gr-qc↗

arXiv2026

Reflectionless and echo modes in asymmetric Damour-Solodukhin wormholes

It is understood that the echo waveforms in ultracompact objects can be regarded as composed mainly of the asymptotic high-overtone quasinormal modes, dubbed echo modes, which predominantly lie parallel to the real frequency axis. Alternatively, Rosato {\it et al.} recently suggested that high-frequency quasi-reflectionless scattering modes are primarily responsible for the echo phenomenon. In this work, by extending the definition of quasi-reflectionless modes to reflectionless ones and generalizing symmetric Damour-Solodukhin wormholes to asymmetric cases, we examine the underlying similarity between the reflectionless and echo mode spectra in the complex frequency plane. Through a primarily analytical treatment, we demonstrate that the asymptotic properties of these two spectra exhibit a strong resemblance, featuring an approximately uniform distribution parallel to the real frequency axis with the same spacing between successive modes. Specifically, the real parts of echo modes coincide with those of reflectionless modes at the limit $|\mathrm{Re}ω| \gg |\mathrm{Im}ω|$. While echo modes typically possess non-vanishing imaginary parts, the reflectionless modes of symmetric Damour-Solodukhin wormholes lie precisely on the real frequency axis, with any deviation serving as a measure of the degree of asymmetry of the wormhole. For a given identical source, the waveforms are calculated numerically using the Green's functions. The amplitudes of the waveforms associated with reflectionless modes are found to be more pronounced than those of the echo modes, because reflectionless modes typically lie closer to the real frequency axis than the latter. It is argued that both perspectives provide effective tools for describing the echo phenomenon.

gr-qc↗

arXiv2026

On the mapping between bound states and black hole quasinormal modes via analytic continuation: a spectral instability perspective

In this work, we investigate the relation between bound states and quasinormal modes within black hole perturbation theory in the context of spectral instability. Our analysis indicates that the reliability of such spectral mapping stretches beyond the domain of validity of the analytic continuation employed to connect the perturbative bound-state problem to the corresponding open-system dynamics. However, for the numerical scheme proposed by Völkel to work, the transformations of the metric parameters must be carried out in a region where the underlying Taylor expansion is convergent. As analytically accessible explicit examples, we explore the perturbed delta-function and Pöschl-Teller potential barriers. For the latter, we construct two distinct perturbative setups for which the convergence of the series expansion involved in the perturbation theory can be rigorously controlled. When the deformation is placed near the potential's extremum, the resulting corrections to the bound-state energies can be analytically continued to yield perturbed quasinormal frequencies, in agreement with known semi-analytic results. In contrast, when the perturbation is localized asymptotically far from the compact object, the bound states are only mildly modified and are accurately described by a perturbative expansion to the first order. However, the associated analytic continuation yields a strongly deformed spectrum that shows no clear connection to the quasinormal modes. These findings contribute to the effort to scrutinize the conditions under which bound states faithfully encode quasinormal spectra and to shed light on the underlying physics of black hole spectral instability.

gr-qc↗

arXiv2026

Continued fraction method for high overtone quasinormal modes in effective potentials with discontinuity

In this study, we extend Leaver's continued fraction method to evaluate black hole quasinormal modes (QNMs) in systems where the effective potential exhibits a discontinuity. Besides the low-lying modes, we particularly focus on high overtones, which are physically pertinent due to the substantial deformation of the QNM spectrum triggered by spectral instability. In our algorithm, we expand the wavefunction at the point of discontinuity, instead of the black hole horizon, and incorporate the Israel-Lanczos-Sen junction conditions. %As the wavefunction convergence condition becomes irrelevant, our proposed algorithm generalizes the original method by expanding the wavefunctions at the point of discontinuity, and the associated difficulty is mitigated by rectifying the recurrence relations between the expansion coefficients to incorporate the Israel-Lanczos-Sen junction conditions. We apply this algorithm to compute the QNMs of the modified Regge-Wheeler potential up to $2000$ modes with high precision. For the low-lying modes, the numerical results show excellent agreement with those obtained using the matrix and Prony methods. The high overtones are significantly deformed, owing to the presence of echoes due to the discontinuity. This deformation in the asymptotic QNM spectrum reveals universal features that are largely independent of the specific form of the discontinuity in the potential, seemingly coinciding with those observed in the modified Pöschl-Teller effective potential. We speculate on whether the collective effect of the high overtones has an observational impact on gravitational wave signals.

gr-qc↗

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 Pöschl-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↗

arXiv2026

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↗

arXiv2026

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

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

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

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 bifurcation and spectral instability of asymptotic quasinormal modes in the modified Pöschl-Teller effective potential

The Pöchl-Teller effective potential mimics an asymptotically de Sitter black hole bounded by an event horizon and a cosmological one. Owing to the benefit of being analytically soluble, the asymptotic quasinormal modes in the modified Pöschl-Teller potential have been extensively explored in the literature by various authors, and the results bear distinct features. Specifically, for small discontinuities placed at the potential's peak, Skakala and Visser showed that the resulting modes lie primarily along the imaginary frequency axis, in line with the numerical results encountered for most black hole metrics. However, it was also suggested that under ultraviolet perturbations, asymptotic modes are expected to lie parallel to the real axis, closely intervening with recent developments on spectral instability. In this work, by numerical and semi-analytical approaches, we aim to resolve the above apparent ambiguity. The numerical scheme is based on an improved version of the matrix method, which is implemented in compactified hyperboloidal coordinates on the Chebyshev grid. It is demonstrated that both asymptotic behaviors indeed agree with the numerical findings, which is somewhat to one's surprise. Specifically, we report the emergence of a novel branch of purely imaginary modes originating from a bifurcation in the asymptotic quasinormal mode spectrum. Moreover, we demonstrate how the bifurcation and asymptotic modes evolve as the discontinuity moves away from the potential's peak, furnishing a dynamic picture as the spectral instability unfolds. It is further argued that they can be partly attributed to the observed parity-dependent deviations occurring for the low-lying perturbed modes of the original Pöschl-Teller effective potential.

gr-qc↗

arXiv2024

Calculating quasinormal modes of extremal and non-extremal Reissner-Nordström black holes with the continued fraction method

We use the numerical continued fraction method to investigate quasinormal mode spectra of extremal and non-extremal Reissner-Nordström black holes in the low and intermediate damping regions. In the extremal case, we develop techniques that significantly expand the calculated spectrum from what had previously appeared in the literature. This allows us to determine the asymptotic behavior of the extremal spectrum in the high damping limit, where there are conflicting published results. Our investigation further supports the idea that the extremal limit of the non-extremal case, where the charge approaches the mass of the black hole in natural units, leads to the same vibrational spectrum as in the extremal case despite the qualitative differences in their topology. In addition, we numerically explore the quasinormal mode spectrum for a Reissner-Nordström black hole in the small charge limit.

gr-qc↗

arXiv2024

Spacetime metrics and ringdown waveforms for galactic black holes surrounded by a dark matter spike

Theoretical models suggest the existence of a dark matter spike surrounding the supermassive black holes at the core of galaxies. The spike density is thought to obey a power law that starts at a few times the black hole horizon radius and extends to a distance, $R_\text{sp}$, of the order of a kiloparsec. We use the Tolman-Oppenheimer-Volkoff equations to construct the spacetime metric representing a black hole surrounded by such a dark matter spike. We consider the dark matter to be a perfect fluid, but make no other assumption about its nature. The assumed power law density provides in principle three parameters with which to work: the power law exponent $γ_\text{sp}$, the external radius $R_\text{sp}$, and the spike density $ρ_\text{DM}^\text{sp}$ at $R_\text{sp}$. These in turn determine the total mass of the spike. We focus on Sagittarius A* and M87 for which some theoretical and observational bounds exist on the spike parameters. Using these bounds in conjunction with the metric obtained from the Tolman-Oppenheimer-Volkoff equations, we investigate the possibility of detecting the dark matter spikes surrounding these black holes via the gravitational waves emitted at the ringdown phase of black hole perturbations. Our results suggest that if the spike to black hole mass ratio is roughly constant, greater mass black holes require relatively smaller spike densities to yield potentially observable signals. We find that is unlikely for the spike in M87 to be detected via the ringdown waveform with currently available techniques unless its mass is roughly an order of magnitude larger than existing observational estimates. However, given that the signal increases with black hole mass, spikes might be observable for more massive galactic black holes in the not too distant future.

astro-ph.GA↗

arXiv2022

Calculating quasinormal modes of Schwarzschild anti-de Sitter black holes using the continued fraction method

We investigate the scalar, gravitational, and electromagnetic quasinormal mode spectra of Schwarzschild anti-de Sitter black holes using the numerical continued fraction method. The spectra have similar, almost linear structures. With a few exceptions, the low overtone quasinormal modes are consistent with previously obtained results in the literature that use other numerical techniques. The intermediate and high overtone quasinormal modes, in comparison to the Schwarzschild case, converge very quickly to the asymptotic formulas previously obtained by analytic monodromy techniques. In addition, we find a connection between the analytic asymptotic formulas and the purely imaginary modes. In particular, these formulas can be used to predict the bifurcation of the lowest damped electromagnetic modes. Finally, we find no high overtone quasinormal modes with high oscillation frequency and low damping, which had been previously predicted.

gr-qc↗

arXiv2022

Gravitational and electromagnetic radiation from an electrically charged black hole in general nonlinear electrodynamics

We derive the equations for the odd and even parity perturbations of coupled electromagnetic and gravitational fields of a black hole with an electric charge within the context of general nonlinear electrodynamics. The Lagrangian density is a generic function of the Lorentz invariant scalar quantities of the electromagnetic fields. We include the Hodge dual of the electromagnetic field tensor and the cosmological constant in our calculations. For each type of parity, we reduce the system of Einstein field equations coupled to nonlinear electrodynamics to two coupled Schrödinger-type wave equations, one for the gravitational field and one for the electromagnetic field. The stability conditions in the presence of the Hodge dual of the electromagnetic field are derived.

gr-qc↗