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Liang-Bi Wu

Publications and source records attributed to Liang-Bi Wu.

30 records · Page 2Linked to original sources
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 (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 ($\text{Im} ω<0$), 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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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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arXiv2025

The stability of the greybody factor of Hayward black hole

In this study, we investigate the stability of the greybody factor of Hayward black holes by adding a small bump to the effective potential. Since the greybody factor depends on frequency, we introduce the $\mathcal{G}$-factor and $\mathcal{H}$-factor to quantitatively characterize its stability. We study the stability of the greybody factor within the equal amplitude method and the equal energy method, respectively. Here, the equal amplitude method can be directly imposed by fixing the amplitude of the bump, while the equal energy method requires a physical definition of the energy of the bump with the assistance of hyperboloidal framework. For both methods, when the location of the bump is close to the event horizon of the black hole, and the closer it is to the peak of the original potential, the larger are $\mathcal{G}$-factor and $\mathcal{H}$-factor, and they are bounded by the magnitude of the amplitude or the energy. More importantly, for the equal amplitude method, two factors tend to a specific value as the location of the bump increases. In contrast, for the equal energy method, two factors converge to zero as the location of the bump increases. Notably, the $\mathcal{G}$-factor and the $\mathcal{H}$-factor are insensitive to the regular parameter of Hayward black hole. Therefore, our results indicate that the greybody factor is stable under specific perturbations.

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arXiv2024

The pseudospectrum and transient of Kaluza-Klein black holes in Einstein-Gauss-Bonnet gravity

The spectrum and dynamical instability, as well as the transient effect of the tensor perturbation for the so-called Maeda-Dadhich black hole, a type of Kaluza-Klein black hole, in Einstein-Gauss-Bonnet gravity have been investigated in framework of pseudospectrum. We cast the problem of solving quasinormal modes (QNMs) in AdS-like spacetime as the linear evolution problem of the non-normal operator in null slicing by using ingoing Eddington-Finkelstein coordinates. In terms of spectrum instability, based on the generalised eigenvalue problem, the QNM spectrum and $ε$-pseudospectrum has been studied, while the open structure of $ε$-pseudospectrum caused by the non-normality of operator indicates the spectrum instability. In terms of dynamical instability, we introduce the concept of the distance to dynamical instability, which plays a crucial role in bridging the spectrum instability and the dynamical instability. We calculate such distance, named the complex stability radius, as parameters vary. Finally, we show the behaviour of the energy norm of the evolution operator, which can be roughly reflected by the three kinds of abscissas in context of pseudospectrum, and find the transient growth of the energy norm of the evolution operator.

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arXiv2024

The pseudospectrum and spectrum (in)stability of quantum corrected Schwarzschild black hole

In this study, we investigate the pseudospectrum and spectrum (in)stability of quantum corrected Schwarzschild black hole. Methodologically, we use the hyperboloidal framework to cast the quasinormal mode (QNM) problem into an eigenvalue problem associated with a non-selfadjoint operator, and then the spectrum and pseudospectrum are depicted. Besides, the invariant subspace method is exploited to improve the computational efficiency for pseudospectrum. The investigation into the spectrum (in)stability entails two main aspects. On the one hand, we calculate the spectra of the quantum corrected black hole, then by the means of the migration ratio, the impact of the quantum correction effect on the Schwarzschild black hole has been studied. The results indicate that the so-called ``migration ratio instability" will occur for small black holes with small angular momentum number l. In the eikonal limit, the migration ratios remain the same for each overtone. On the other hand, we study the spectrum (in)stability of the quantum corrected black hole by directly adding some particular perturbations into the effective potential, where perturbations are located at the event horizon and null infinity, respectively. There are two interesting observations under the same perturbation energy norm. First, perturbations at infinity are more capable of generating spectrum instability than those at the event horizon. Second, we find that the peak distribution can lead to the instability of QNM spectrum more efficiently than the average distribution.

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arXiv2024

The instability of the inner horizon of the quantum-corrected black hole

We analyse the stability of the inner horizon of the quantum-corrected black hole which is proposed in loop quantum gravity as the exterior of the quantum Oppenheimer-Snyder and Swiss Cheese models. It is shown that the flux and energy density of a test scalar field measured by free-falling observers are both divergent near the Cauchy horizon. By considering the generalized Dray-'t Hooft-Redmond relation which is independent of the field equation, we find that the mass inflation always happens and the scalar curvature and Kretschmann scalar are also divergent on the inner horizon. These suggest that the inner horizon is unstable and will probably turn into a null singularity. The results support the strong cosmic censorship hypothesis. However, this also implies that the quantum corrected model may not be the definitive endpoint as a regular black hole. Besides, it further proposes that it may be challenging to observe the astronomical phenomenon which depends on the existence of the inner horizon of the black hole.

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arXiv2023

Constraint preserving boundary conditions in Bondi-Sachs gauge: a numerical study of stability of pure AdS spacetime

In the Bondi-Sachs gauge, the Einstein equations with a cosmological constant coupled to a scalar field in spherical symmetry are cast into a first order strongly hyperbolic formulation in which the lapse and shift are the fundamental variables. For this system of equations, the lapse and shift are ingoing characteristic fields, and the scalar field has three modes: ingoing, outgoing and static, respectively. A constraint-preserving initial boundary value problem is constructed by using Bianchi identity. Using this scheme, we find that any small perturbation of the scalar field at the boundary far away enough can cause the collapse of the pure AdS spacetime, and we provide the numerical evidence for the formation of apparent horizons. The numerical evolution is performed with a standard method of lines, second order in space and time. The evolution is performed using the standard second order Runge-Kutta method while the space discrete derivative is second order central difference with fourth order artificial dissipation.

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arXiv2021

A Note on the Strong Hyperbolicity of $f(R)$ Gravity with Dynamical Shifts

The well-posedness of the gravitational equations of $f(R)$ gravity are studied in this paper. Three formulations of the $f(R)$ gravity with dynamical shifts (which are all based on the Arnowitt-Deser-Misner (ADM) formalism of the equations) are investigated. These three formulations are all proved to be strongly hyperbolic by pseudodifferential reduction. The first one is the Baumagarte-Shapiro-Shibata-Nakamura (BSSN) formulation with the so-called "hyperbolic $K$-driver" condition and the "hyperbolic Gamma driver" condition. The second one is the ADM formulation with modified harmonic gauge conditions. We find that the equations are not strong hyperbolic in traditional Z4 formulation for $f(R)$ gravity. So, in the third formulation, we improve the Z4 formulation, and show these equations are strong hyperbolic with modified harmonic gauge conditions.

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arXiv2021

A Bound on the Rate of Bondi Mass Loss

To ensure the light (emitted far away from the source of gravity) can arrive at the null infinity of an asymptotically flat spacetime, it is shown that the rate of Bondi mass aspect has to satisfy some conditions. In Einstein gravity theory, we find the sufficient condition implies a bound on the Bondi mass $m$, i.e., $|\dot{m}|\leqslant 0.3820~c^3/G$. This provides a new perspective on Dyson's maximum luminosity. However, in Brans-Dicke theory, the sufficient condition depends on the behavior of the radiation field of the scalar. Specifically, the photons can escape to the null infinity when the scalar gravitational radiation is not too large and the mass loss is not too fast.

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arXiv2021

Hyperbolicity and Causality of Einstein-Gauss-Bonnet Gravity in Warped Product Spacetimes

In Einstein-Gauss-Bonnet gravity, for a group of warped product spacetimes, we get a generalized master equation for the perturbation of tensor type. We show that the "effective metric" or "acoustic metric" for the tensor perturbation equation can be defined even without a static condition. Since this master equation does not depend on the mode expansion, the hyperbolicity and causality of the tensor perturbation equation can be investigated for every mode of the perturbation. Based on the master equation, we study the hyperbolicity and causality for all relavent vacuum solutions of this theory. For each solution, we give the exact hyperbolic condition of the tensor perturbation equations. Our approach can also applied to dynamical spacetimes, and Vaidya spacetime have been investigated as an example.

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