arXiv subjects

Liang-Bi Wu

Publications and source records attributed to Liang-Bi Wu.

At least 19 recordsLinked to original sources

arXiv2026

The (in)stability on total transmission modes with small bumps

Total transmission modes (TTMs) are a class of reflectionless solutions to black hole perturbation equations, closely related to quasinormal modes (QNMs), and can exhibit significant sensitivity to weak environmental perturbations. In this work, we investigate the spectrum (in)stability of TTMs of Tangherlini black holes by introducing a localized P\"{o}schl-Teller bump perturbation into the effective potential, and employ a modified Chebyshev-Lobatto grid to improve the numerical accuracy of the localized perturbation. For $d=14$, $\ell=2$, and $s=2$, the purely imaginary TTM exhibits relatively strong spectrum stability, whereas the genuine complex TTMs undergo significant migrations even for small perturbations, consistent with the spectrum stability revealed by previous pseudospectrum analyses.

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arXiv2026

Global structure and stability of Kerr-Bertotti-Robinson spacetime

The surface $r=\infty$ of the Kerr-Bertotti-Robinson spacetime is not a genuine boundary. We construct its natural analytic extension and show that $r=+\infty$ of one KBR region is smoothly connected to $r=-\infty$ of a neighboring one. Repeated continuation produces an infinite chain of regions connected by wormhole-like bridges and exposes the neighboring ring singularity without an intervening horizon, which violates the weak cosmic censorship conjecture. We then study a test massless scalar field on a two-universe scattering segment to probe the stability of the spacetime. For axisymmetric perturbations, we analytically establish purely imaginary growing quasinormal modes for every $\ell$ and trace their origin to the chronology-violating region. In the $(\ell,m)=(2,2)$ sector, unstable branches occur for sufficiently large rotation and sufficiently small magnetic field. Their marginal real modes obey an exact horizon-flux balance, supporting a black-hole-bomb interpretation in which superradiant extraction is amplified by trapping within the double-barrier potential. The same cavity also supports families of weakly damped modes and may produce echo-like responses.

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arXiv2026

Notes on Kerr-Bertotti-Robinson Spacetime

The surface $r=\infty$ of the Kerr--Bertotti--Robinson (KBR) spacetime is not the collection of the endpoints of infinitely extended light rays, and the Coulomb type component of gravitational field strength represented by $\Psi_2$ remains nonvanishing there, indicating that this surface is not a real boundary. We construct a natural extension across this surface, which connects the exterior of one KBR region to the interior of a neighboring one and, upon iteration, produces an infinite chain of regions connected by wormhole-like bridges. The extension also exposes the neighboring ring singularity without an intervening horizon, challenging the weak cosmic censorship conjecture and raising the question of whether the extended geometry is stable under perturbations. We therefore study the quasinormal modes (QNMs) of a test massless scalar field on a two-universe scattering segment. For axisymmetric perturbations, the existence of purely imaginary unstable QNMs is analytically proved for every $\ell$, with their origin tied to the chronology-violating region. In the $(\ell,m)=(2,2)$ sector, unstable QNM branches driven by a black-hole-bomb mechanism are found. Finally, the wormhole geometry produces a double-barrier cavity and families of weakly damped QNMs, suggesting echo-like responses.

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arXiv2026

Exceptional lines of Reissner-Nordstr\"{o}m-de Sitter black hole surrounded by a thin shell of matter

We study the exceptional line (EL) in the quasinormal modes (QNMs) of Reissner-Nordstr\"{o}m-de Sitter black hole surrounded by a static thin shell of matter. For a conformally scalar perturbation, we derive the QNM condition by matching the interior and exterior solutions across the shell and show that higher overtones are particularly sensitive to variations of the shell and background parameters. A mode permutation between two QNMs reveals an exceptional point (EP). After extending the parameter space, this degeneracy forms a continuous EL. We show that the spectral response near the line is intrinsically directional. For a perturbation in parameter space $\epsilon\widehat{\mathbf u}$, the QNM splitting is $|\omega_+-\omega_-| =C_{\widehat{\mathbf u}}\sqrt{\epsilon}+o(\sqrt{\epsilon})$, with $C_{\widehat{\mathbf u}}=(\widehat{\mathbf u}^{T}\mathbf{K}\widehat{\mathbf u})^{1/4}$ and $\mathbf{K}$ is so-called spectral sensitivity anisotropy matrix. The tangent direction of EL is a null direction of $\mathbf{K}$, so that the leading square-root splitting vanishes along the exceptional line, whereas the two principal directions in the normal plane exhibit different sensitivities. Furthermore, the square-root branch structure makes conventional linear QNM parametrizations singular near an EL. We therefore construct an EL adapted parametrization which incorporates both the local geometry of the line and the nonanalytic QNM splitting.

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arXiv2026

Extended parameterized spin expansion formalism for ringdown analysis with GW250114

Parameterized descriptions of black-hole quasinormal-mode spectra are essential for testing gravity with ringdown observations. We extend the Parameterized Spin Expansion Coefficients (ParSpec) formalism by simultaneously sampling the characteristic length scale $\tilde{\ell}$ and the scaling index $\tilde{p}$, rather than fixing $\tilde{p}$ to a theory-motivated integer and constraining $\ell$. Physically, this extension promotes the scaling of the spectral corrections coming from higher-curvature operators to an observable quantity. Methodologically, it enables us to investigate the enlarged ParSpec parameter space and identify the prior geometry induced by conditions on the effective coupling $\gamma$. We examine the robustness of the framework by using the $220$ and $220+221$ ringdown models over different start times with informative priors on mass and luminosity for GW250114, and further study a joint constraint with GW231123. We find that $\tilde{p}$ remains prior dominated and that the data show no evidence for deviations from general relativity (GR). Among the coupling prescriptions considered, $\gamma<1$ avoids an artificial correlation between $\tilde{p}$ and $\tilde{\ell}$. At the current signal-to-noise ratio, the results based on the Kullback-Leibler divergence show that the $220$-only model provides more informative constraints than the $220+221$ model. Higher-SNR ringdowns and hierarchical analyses of a larger event population will be required to break the $\tilde{p}-\tilde{\ell}$ degeneracy and directly probe the scaling structure of corrections to GR.

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arXiv2026

Total transmission modes in draining bathtub model with vorticity

We investigate the total transmission modes (TTMs) in the draining bathtub model (DBM) with vorticity using the Chebyshev-Lobatto pseudospectral method, where the boundary conditions of the total transmission modes are both ingoing at the event horizon and infinity. Numerical results show that the (right) TTM spectra can possess positive imaginary parts, while for certain parameters they acquire negative imaginary parts. The extreme sensitivity of the higher overtones is manifested as their pronounced spectral mobility.

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arXiv2026

Virtual absorption modes of Schwarzschild-de Sitter spacetimes in semi-open systems

We present a study of virtual absorption modes (VAMs) in Schwarzschild-de Sitter (SdS) spacetime under semi-open boundary conditions, where the VAMs correspond to total transmission modes (TTMs) with the reflection amplitude being vanished. Our numerical analysis reveals that as the reflectivity $|\mathcal{K}|$ decreases, the VAM spectra migrate systematically toward regions of less negative imaginary parts, with each overtone exhibiting a critical reflectivity at which $\text{Im}(\omega_{\text{VAM}})=0$. Using simulations based on spectral collocation methods, it is demonstrated that excitation precisely at a VAM spectrum leads to coherent perfect absorption (CPA). These results establish VAMs as the spectrum signatures of CPA for exotic compact objects (ECOs).

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arXiv2025

Pseudospectrum and (in)stability of black hole total transmission modes

Total transmission modes (TTMs) are modes with complex frequencies that propagate across a black hole spacetime without reflection. Recently, it is found that suitably tailored time-dependent scattering can excite these complex modes and suppress the reflected signal for the entire duration of the process, a phenomenon referred to as virtual absorption. Motivated by this, we present a study of the spectrum stability of TTMs using pseudospectrum and condition numbers. We focus on perturbations of $d$-dimensional Tangherlini black holes and recast the TTM problem as a generalized eigenvalue problem by utilizing the Eddington-Finkelstein coordinates. The results show that TTMs are generically spectrally unstable, with sensitivity increasing for higher overtones, in close analogy with quasinormal modes. A notable exception is the purely imaginary TTM in the positive imaginary axis in higher dimensions. Its pseudospectrum contours are nearly concentric, and its condition number is orders of magnitude smaller than those of the overtones, indicating enhanced spectral stability. As the spacetime dimension decreases, the condition number grows and becomes much larger in four dimensions in both the energy norm and the $L^2$ norm, suggesting possible spectral instability, although a definitive cross-dimensional conclusion is limited by the lack of a uniform physically preferred norm. Additionally, we confirm that purely imaginary TTMs occur for gravitational vector perturbations, whereas genuinely complex TTM families appear only in sufficiently high dimensions, $d \geqslant 8$, extending earlier claims that placed the onset at $d \geqslant 10$.

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arXiv2025

Quasinormal modes of Schwarzschild-de Sitter black holes in semi-open systems

We study perturbations of Schwarzschild-de Sitter black holes in semi-open systems by using the Heun functions. For the semi-open system, a partially reflective wall is added around the event horizon. Three aspects of this model are investigated, namely the quasinormal mode (QNM) spectra, the greybody factor (GF), and the exceptional point (EP). For the QNM aspect, we identify three distinct behaviors as the frequency-independent reflectivity $\mathcal{K}$ increasing. The first-type modes approach the real axis and form long-lived quasi-bound states. The second-type modes move toward but do not reach the real axis and retain a finite decay rate. The third-type modes eventually lie on the imaginary axis becoming purely decaying modes. For the GF aspect, GFs exhibit strong oscillations controlled by the distance between the potential and the reflective wall with a real constant reflectivity. In contrast, a Boltzmann-type reflectivity produces only small corrections. Finally, by promoting $\mathcal{K}$ to a complex parameter, the modified boundary conditions give rise to a second-order EP. Parameterizing the vicinity of such EP, we observe the mode exchange phenomenon, and the deviation of spectra scale with the square root of the deviation of the parameter, as predicted by a Puiseux series expansion.

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arXiv2025

Exceptional line and pseudospectrum in black hole spectroscopy

We investigate the exceptional points (EPs) and their pseudospectra in black hole perturbation theory. By considering a Gaussian bump modification to the Regge-Wheeler potential with variable amplitude, position, and width parameters, $(\varepsilon,d,\sigma_0)$, a continuous line of EPs (exceptional line, EL) in this three-dimensional parameter space is revealed. Notably, the EL exhibits an anisotropic spectral response: parameters migrating along the EL direction leaves the coalesced QNM spectra nearly unchanged, while moving parameters away from the EL induces the characteristic $\epsilon^{1/2}$ scaling, highlighting the directional nature of spectral instability in exceptional structures. We find that the vorticity $\nu=\pm1/2$ and the Berry phase $\gamma=\pi$ for loops encircling the EL, while $\nu=0$ and $\gamma=0$ for those do not encircle the EL. In the neighborhood of an eigenvalue, through matrix perturbation theory, we prove that the $\epsilon$-pseudospectrum contour size scales as $\epsilon^{1/q}$ at an EP , where $q$ is the order of the largest Jordan block of the Hamiltonian-like operator associated with that eigenvalue, contrasting with the linear $\epsilon$ scaling at non-EPs. Numerical implements confirm this observation, demonstrating enhanced spectral instability at EPs for non-Hermitian systems including black holes.

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arXiv2025

The parameterized quasinormal modes for modified Teukolsky equations

We introduce the modified Teukolsky equation within a parameterized framework, analogous to the case of small deviations of potential in spherical symmetry. Both the radial and angular equations acquire modifications described by two independent sets of parameters. We derive the parameterized framework of the quasinormal mode spectra using the continued fraction method. The results are cross-validated with the two-dimensional pseudo-spectral method, demonstrating excellent agreement and ensuring self-consistency. This work establishes a robust foundation for a theory-agnostic interpretation of gravitational-wave ringdown signals, providing a practical tool for probing potential deviations from General Relativity in the strong-field regime.

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arXiv2025

The quasinormal modes of the rotating quantum corrected black holes

The quasinormal modes (QNMs) of a rotating quantum corrected black hole (RQCBH) are studied by employing the hyperboloidal framework for the scalar perturbation. This framework is used to cast the QNMs spectra problem into a two-dimensional eigenvalue problem, then the spectra are calculated by imposing the two-dimensional pseudo-spectral method. Based on the resulting scalar spectra, a parameter estimation pipeline for this RQCBH model with gravitational wave data is constructed by using \texttt{pyRing} in the ringdown phase. We use informative priors in our inference that incorporates the mass and spin distributions predicted by the inspiral-merger phase as the prior distributions for the ringdown analysis. Notably, since the waveform model beyond Kerr black hole in $\texttt{pyRing}$ is designed for the tensor perturbation, the inferred posterior distributions should be interpreted as a methodological investigation rather than as physical constraints from observations. The methodological results show that the use of informative priors consistently yields a tighter posterior on the quantum correction parameter compared to analyses without such priors, and the spin inferred from the RQCBH model begins to be significant and differs from that of the Kerr model. This opens a promising avenue for testing quantum-gravity-induced deviations using gravitational-wave spectroscopy.

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arXiv2025

QNM families: classification and competition

The perturbation spectra of black holes beyond standard vacuum black hole solutions within generalrelativity (GR) may exhibit complex structures with long-lived modes. This usually generates echolikemodulations on the ringdown signal, which typically originate from modified boundary conditionsassociated with exotic compact objects. Recent studies also reveal that they can instead arise from themultipeaked structure of the perturbation potential. However, while some case-by-case studies have beencarried out, a framework for understanding the internal structure of such spectra, the physical nature ofdifferent mode families, and their dynamical excitation remains to be fully systematized. In this paper,we address this issue by proposing a potential methodology that combines frequency-domainclassification with time-domain analysis, using a hairy Schwarzschild black hole that admits adouble-peak perturbative potential as a theoretical platform. Our analysis of the quasinormal modespectrum identifies two distinct families of modes: the photon sphere (PS) family, arising fromdelocalized scattering resonances, and the echo family, corresponding to highly localized quasiboundstates. We then develop a windowed energy analysis framework in the time domain, which discloses adynamic competition for dominance between these families. In particular, our results explicitly showthat this competition is sensitive to the properties of the initial perturbation source, and that higher-overtone echo modes can dominate in the observed signal, which are in contrast to the standard PS modein GR. This study establishes the dynamic evolution of this energy competition as a new observationalsignature for probing new physics and further motivates a supplemental framework for analyzing long-lived ringdown signals.

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arXiv2025

Waveform stability for the piecewise step approximation of Regge-Wheeler potential

By interpreting the difference between the original Regge-Wheeler potential and its piecewise step approximation as perturbative effects induced by the external environment of the black hole, we investigate the stability of Schwarzschild black hole time-domain waveforms. In this work, we employ the Green's function method under the assumption of an observer at spatial infinity to obtain the waveform. For two cases in which the initial Gauss bump near the event horizon or at spatial infinity, we derive analytic expressions for the corresponding waveforms. Our results demonstrate that the waveform is indeed insensitive to tiny modifications of the effective potential, thereby confirming its stability. More importantly, we find that broader initial bumps imprint the influence of small environmental modifications more clearly on the waveform, which may provide theoretical guidance for probing the exterior environment of black holes.

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arXiv2025

Pseudospectrum and time-domain analysis of the EFT corrected black holes

We study the linear perturbations of a spherically symmetric black hole corrected by dimension-6 terms in the effective field theory (EFT) of gravity. The solution is asymptotically flat and characterized by two parameters -- a mass parameter $M$ and a dimensionless parameter $\varepsilon$ related to the EFT length scale $l$, and the perturbation equation incorporates a velocity factor which is not constant. The quasinormal modes (QNMs) and time-domain waveforms are studied within the hyperboloidal framework. This approach reproduces the breakdown of the isospectrality and reveals that higher overtones are more sensitive to $\varepsilon$. As for the time domain, the mismatch function is introduced and found to scale as $\varepsilon^2$, which demonstrates that the waveform is stable as $\varepsilon$ varies. Finally, a velocity-dependent energy norm is employed to compute the pseudospectrum and characterize the migration of the QNM spectrum. We further define a quantity $\epsilon_c$ that describes the magnitude of the instability of a QNM spectrum. Our analysis reveals that the dependence of $\epsilon_c$ on $\varepsilon$ is complicated -- it may increase, decrease or even be nonmonotonic.

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arXiv2025

Spectrum instability and greybody factor stability for parabolic approximation of Regge-Wheeler potential

We investigate the stability of QNM spectra and greybody factors in the Schwarzschild black hole by approximating the Regge-Wheeler potential with a piecewise parabolic form and treating the deviation as a perturbation. We find that QNM spectra are sensitive to small perturbations, while greybody factors remain stable. This piecewise parabolic approximated potential gives rise to the long-lived modes whose imaginary parts remain close to zero and decrease slowly with overtone number increasing. The reflection coefficient shows distinct resonance feature in the high-frequency regime that are absent in the original R-W case. For the calculation of greybody factors, we employ an analytic method based on transfer matrix technique, and this approach can also be effectively used in other effective potential cases.

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arXiv2025

The pseudospectrum for the Kerr black hole with spin $s=0$ case

We investigate the pseudospectrum of the Kerr black hole, which indicates the instability of the spectrum of quasinormal modes (QNMs) of the Kerr black hole. Methodologically, we use the hyperboloidal framework to cast the QNM problem into a two-dimensional eigenvalue problem associated with a non-self-adjoint operator, and then the spectrum and pseudospectrum are solved by imposing the two-dimensional Chebyshev collocation method. The (energy) norm is constructed by using the conserved current method for the spin $s=0$ case. For the finite rank approximation of the operator, we discuss the convergence of pseudospectra using various norms, each involving different orders of derivatives. The convergence of the pseudospectrum improves as the order of the derivatives increases. We find that an increase in the imaginary part of complex frequency can deteriorate the convergence of the pseudospectrum under the condition of the same norms.

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arXiv2024

The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework

We study the quasinormal modes of Boulware-Deser-Wheeler black hole in Einstein-Gauss-Bonnet gravity theory within the hyperboloidal framework. The effective potentials for the test Klein-Gordon field and gravitational perturbations of scalar, vector, and tensor types are thoroughly investigated and put into several typical classes. The effective potentials for the gravitational perturbations have more diverse behaviors than those in general relativity, such as double peaks, the existence of the negative region adjacent to or far away from the event horizon, etc. These lead to the existence of unstable modes ($\text{Im} \omega<0$), and the presence of gravitational wave echoes. These rich phenomenons are inherent in Einstein-Gauss-Bonnet theory, rather than artificially introduced by hand. What's more, the (in)stability of quasinormal modes is studied in frequency domain and time domain, respectively. For the frequency-domain, the pseudospectrum is used to account for the instability of the spectrum. For the time-domain, we add a small bump to the effective potential, and find that the new waveform does not differ significantly from the original one, where the comparison is characterized by the so-called mismatch functions. This means that quasinormal modes are stable in time-domain regardless of the shapes of the original effective potentials. In this way, our study reveals the non-equivalence of the stability of quasinormal modes in the frequency-domain and the time-domain. Besides, we also numerically investigate Price's law at both finite distances and infinity with the assistance of the hyperboloidal approach.

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