arXiv subjects

Chen Lan

Publications and source records attributed to Chen Lan.

At least 19 recordsLinked to original sources

arXiv2026

Darboux Isospectrality Constraints on Quasinormal Modes Deformed by Bumps

A localized Gaussian or P\"oschl-Teller bump is widely used to probe the sensitivity of Schwarzschild quasinormal modes, where it is typically added to both the Regge-Wheeler and Zerilli potentials. We show that such an additive prescription is generically incompatible with the Darboux transformation connecting the two parity sectors. The reason is that such a transformation restricts a parity-blind bump to a fixed family of bumps with an unavoidable $r^{-2}$ tail, excluding any Gaussian or P\"oschl-Teller profile with arbitrary amplitude, center, or width in the additive prescription. We give the complete classification of Darboux-admissible axial and polar pairs of bumps and propose two consistent scenarios: Darboux generator prescription in which a Gaussian or P\"oschl-Teller profile is retained as a generator of the bump pair rather than as the bump itself, and Riccati completion prescription in which a Gaussian or P\"oschl-Teller profile is regarded as one of the bump pair and its partner will be solved from the Riccati equation. Our frequency-domain calculations confirm that a finite and spurious axial-polar splitting of quasinormal modes will be produced if the Darboux-consistent scenarios are absent, while the centroid shift of the fundamental mode is nearly unchanged.

gr-qc↗

arXiv2026

Kubo-Martin-Schwinger conditions for non-Hermitian systems

We investigate the extension of the Kubo--Martin--Schwinger (KMS) thermal equilibrium condition to bounded non-Hermitian Hamiltonians with real spectra and biorthogonal eigensystems, providing a unified framework through three complementary constructions: a complete KMS theorem under quasi-Hermiticity, a biorthogonal KMS-type identity whose positivity characterises quasi-Hermiticity, and a quantum-detailed-balance condition for the associated open-system dynamics. Our main result is a thermodynamic characterisation of quasi-Hermiticity: for any diagonalisable $H\in M_d(\mathbb C)$ with real spectrum, the biorthogonal Gibbs functional $\omega_{\rm bi}(A)=Z_{\rm bi}^{-1}\sum_n e^{-\beta E_n}\langle\phi_n|A|\psi_n\rangle$ satisfies $\omega_{\rm bi}(A^\dagger A)\ge0$ for all $A$ if and only if $H$ is quasi-Hermitian. The proof reconstructs the metric $\eta$ directly from the eigenprojectors of $\omega_{\rm bi}$ via the Riesz representation theorem, yielding a metric-free criterion for quasi-Hermiticity. Under the quasi-Hermitian hypothesis, we prove that the $\eta$-Gibbs state $\omega_\eta(A)=Z_\eta^{-1}{\rm Tr}[\eta e^{-\beta H}A]$ satisfies the full analytic KMS condition using the Hadamard three-line theorem and Bari's theorem on Riesz bases. The transported state generally differs from the Gibbs state of the isospectral Hermitian partner whenever $[\eta,h]\neq0$, so the KMS property cannot be obtained by similarity transformation alone. Finally, within the Haag--Hugenholtz--Winnink programme, we establish the Tomita--Takesaki modular structure of the $\eta$-Gibbs state in finite dimensions, while the construction of a compatible $C^*$-norm and the proof of $\sigma$-weak continuity remain open.

quant-ph↗

arXiv2026

Parametric resonance amplification of gravitational waves in dynamical Chern-Simons gravity

Within the effective field theory of dynamical Chern-Simons (dCS) gravity, we study parametric resonance amplification of gravitational waves driven by an oscillating environmental field coupled to the dCS pseudoscalar. We find that the black hole potential barrier and external shell form a resonant cavity, producing a Mathieu instability whose optimal frequency is fixed by the cavity length. The instability shows a horizon leakage threshold, Floquet sidebands, and a delayed secondary burst in axial gravitational perturbations. This mechanism reveals that dCS corrections at ultraweak coupling can still accumulate via long term parametric amplification, leaving discernible signatures in gravitational wave signals.

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arXiv2026

No-Go Theorem for Singularity Resolution

We prove a No-Go theorem for singularity resolution in homogeneous, spatially flat gravitational collapse: within this sector, quantum corrections introduced solely as non-vanishing effective matter sources are insufficient to halt singularities in any vacuum-normalized analytic gravitational theory, including general relativity and other theories with analytic gravitational actions. This theorem rules out singularity resolution via effective energy density in a broad class of quantum gravity approaches, including asymptotic safety and noncommutative geometry theories, where the effective energy densities yield finite-time singularities or geodesic incompleteness. The singularity resolution strictly requires non-analytic modifications of the gravitational response at $\mathbb{Q}=0$, or a vanishing effective energy density at high densities (as realized in loop quantum gravity's Planck stars). The theorem is proved via an intrinsic $f(\mathbb{Q})$ gravity framework, extended universally to general relativity, $f(\mathbb{R})$, and $f(\mathbb{T})$ theories through the geometrical trinity at the level of the corresponding homogeneous collapse response structure--with regularity criteria and junction conditions grounded in non-metricity, free of standard GR tools.

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arXiv2026

Branch-dependent ringdown in black-bounce spacetimes: imprints of matter-source ambiguity on quasinormal modes

Regular black holes and black-bounce spacetimes frequently emerge in theoretical frameworks beyond general relativity, as well as in general relativity coupled to non-linear sources. A profound complication in these frameworks is source ambiguity: a single spacetime metric can often be supported by multiple, inequivalent matter-source interpretations, such as an anisotropic fluid or nonlinear electrodynamics (NED) coupled to a scalar field. We investigate how this fundamental degeneracy dynamically imprints on axial gravitational perturbations within the Simpson-Visser spacetime, which smoothly transitions from a regular black hole (BH) to a traversable wormhole (WH) at a critical bounce parameter $a=2M$. By deriving the exact master equations for each interpretation, we perform time-domain numerical evolutions to extract the quasinormal modes (QNMs) via Prony fitting. In the BH branch ($a\le2M$), the NED interpretation exhibits faster QNM damping than the fluid model, driven by enhanced energy leakage through the coupled electromagnetic channel alongside horizon absorption. Conversely, in the WH branch ($a>2M$), the NED coupled system produces longer-lived fundamental modes. This reduced damping is governed by subradiant-like interference that actively suppresses radiative losses to the two asymptotically flat regions. This branch-dependent dynamics, analogous to decay-width redistribution in open non-Hermitian quantum systems, demonstrates that matter-source ambiguity leaves distinct, observable signatures in ringdown waveforms. Our findings establish that gravitational-wave spectroscopy can systematically break the degeneracy of source interpretations, providing a novel empirical pathway to probe the physical nature of exotic compact objects.

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arXiv2025

Parity violating spectral dynamics of black holes in dynamical Chern-Simons gravity

We study how environmentally driven spectral instabilities of quasinormal modes respond to parity violating gravito-scalar coupling in black holes. Focusing on dynamical Chern-Simons gravity as a paradigm for parity violation, we perturb the Schwarzschild background with a localized potential bump. Our analysis reveals three distinctive phenomena absent in general relativity: 1) branch reconnections in the complex frequency plane, 2) a counterintuitive mode stabilization that delays overtaking transitions, and 3) scalar mode dominance emerging at intermediate coupling strengths. These frequency domain features show how comparatively weak static sector differences manifest as distinct dynamical signatures, thereby linking parity violating black hole perturbations with non-Hermitian spectral physics. Our results provide a frequency domain characterization of parity violating coupling and motivate future targeted ringdown studies of modified gravity.

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arXiv2025

The impact of plunging matter on black-hole waveform

In this work, we introduce a novel framework to investigate ringdown gravitational waveforms in the presence of dynamical matter fields outside the horizon of a black hole. We systematically analyze two distinct scenarios of dynamical matter fields: motion along geodesics and uniform motion with constant velocity. Our results reveal rich phenomenology in the ringdown gravitational wave signals, including the suppression or enhancement of echoes, frequency shifts in the decay oscillations, and intricate modulations of the power-law tails. Notably, we demonstrate that subluminal moving potentials can produce irregular echo patterns and shift the dominant frequencies, offering potential new observational signatures beyond the already-known ringdown analyses. This study provides a new perspective for probing dynamic environments around black holes and offers a theoretical foundation for interpreting possible deviations in future gravitational wave detections.

gr-qc↗

arXiv2025

Comment on "Black holes in $f(\mathbb{Q})$ gravity"

In the work [Phys.Rev.D 105 (2022) 2, 024042], D'Ambrosio et al. investigated spherically symmetric black hole solutions in $f(\mathbb{Q})$ gravity, where several solutions satisfy the condition: $g_{tt}g_{rr} = \mathrm{const}$. This condition is characteristic of many black holes, including the Schwarzschild spacetime. In this Comment, we argue that no nontrivial vacuum black hole solutions satisfy this condition in $f(\mathbb{Q})$ gravity. We demonstrate our claim by reexamining the field equations under the "Set 2" connection called by D'Ambrosio et al., which is necessary for obtaining solutions distinct from those of general relativity (GR). For the case where the free parameters $c$ and $k$ are zero, i.e., Option 2 in their work, we show that any attempt to find a solution beyond GR forces the non-metricity scalar to vanish ($\mathbb{Q}=0$), which trivializes the field equations and does not describe a valid black hole solution. Our findings indicate that the condition, $g_{tt}g_{rr} = \mathrm{const.}$, is overly restrictive for finding new, static and spherically symmetric vacuum black holes in $f(\mathbb{Q})$ gravity. This conclusion does not depend on the specific form of $f(\mathbb{Q})$. We also briefly discuss Option 1 that was not addressed in D'Ambrosio et al.'s work, and give new constraints for the selection of parameters $c$ and $k$.

gr-qc↗

arXiv2025

Quasinormal modes of regular black holes surrounded by skewed dark matter distributions

Regular black holes, nonsingular solutions to gravitational collapse with quantum corrections, offer a compelling alternative to classical black holes with curvature singularities. In this work, we investigate how the presence of skewed dark matter distributions outside the innermost stable circular orbit of regular black holes modifies the gravitational wave signals emitted by such objects. Rather than introducing corrections directly into an effective potential, we model the influence of dark matter through metric corrections, allowing a full control over the spatial distribution and abundance of dark matter. We demonstrate that a skewed normal profile generically introduces shallow potential wells or secondary barriers in the effective potential of perturbation equations, depending sensitively on the type of perturbations: scalar, spinor, or tensor. These modifications lead to distinctive quasinormal mode features, including long-lived modes, echo effects, and in some cases, altered stability behaviors. Notably, the axial and polar sectors of tensor field perturbations respond asymmetrically to identical dark matter profiles, revealing a deeper structural distinction in their perturbation dynamics. These results provide a theoretical framework for probing regular black holes in the dark matter environment through gravitational wave observations.

gr-qc↗

arXiv2025

Finite Curvature Construction of Regular Black Holes and Quasinormal Mode Analysis

We develop a class of regular black holes by prescribing finite curvature invariants and reconstructing the corresponding spacetime geometry. Two distinct approaches are employed: one based on the Ricci scalar and the other on the Weyl scalar. In each case, we explore a variety of analytic profiles for the curvature functions, including Gaussian, hyperbolic secant, and rational forms, ensuring regularity, asymptotic flatness, and compatibility with dominant energy conditions. The resulting mass functions yield spacetime geometries free from curvature singularities and exhibit horizons depending on model parameters. To assess the stability of these solutions, we perform a detailed analysis of quasinormal modes (QNMs) under axial gravitational perturbations. We show that the shape of the effective potential, particularly its width and the presence of potential valleys, plays a critical role in determining the QNMs. Models with a large peak-to-valley ratio in the potential barrier exhibit stable, exponentially decaying waveforms, while a small ratio may induce late-time instabilities. Our results highlight the significance of potential design in constructing physically viable and dynamically stable regular black holes, offering potential observational implications in modified gravity and quantum gravity scenarios.

gr-qc↗

arXiv2025

Quantum Corrected Geodesic Motion in Polymer Kerr-like Spacetime

Rotating black holes are prevalent in astrophysical observations, and a Kerr-like solution that incorporates quantum gravity effects is essential for constructing realistic models. In this work, we analyze the geodesic motion of massive particles in a Kerr-like polymer spacetime, incorporating quantum corrections via a parameter $A_\lambda$. We demonstrate that increasing $A_\lambda$ allows for additional orbital evolution in extreme mass ratio inspiral (EMRI) systems before merging. Our results show that the radii, energy, and angular momentum of both the innermost stable circular orbit (ISCO) and marginal circular orbit (MCO) decrease as $A_\lambda$ increases. Furthermore, when the primary object becomes a wormhole, both prograde ISCO and MCO can intersect the transition surface at the wormhole throat and vanish as $A_\lambda$ grows. Additionally, we find that the eccentricity of periodic geodesic motion decreases monotonically with increasing $A_\lambda$. Finally, we explore the variation of the rational number that characterizes periodic motion and highlight the influence of the quantum parameter on different types of periodic orbits, classified by a set of integers associated with the rational number. This work contributes to the understanding of quantum gravity effects and offers potential observational signatures, particularly in the study of EMRIs.

gr-qc↗

arXiv2025

Comparison of Quasinormal Modes of Black Holes in $f(\mathbb{T})$ and $f(\mathbb{Q})$ Gravity

We investigate the quasinormal modes of static and spherically symmetric black holes in vacuum within the framework of $f(\mathbb{Q}) = \mathbb{Q} + \alpha \mathbb{Q}^2$ gravity, and compare them with those in $f(\mathbb{T}) = \mathbb{T} + \alpha \mathbb{T}^2$ gravity. Based on the Symmetric Teleparallel Equivalent of General Relativity, we notice that the gravitational effects arise from non-metricity (the covariant derivative of metrics) in $f(\mathbb{Q})$ gravity rather than curvature in $f(R)$ or torsion in $f(\mathbb{T})$. Using the finite difference method and the sixth-order WKB method, we compute the quasinormal modes of massless scalar field and electromagnetic field perturbations. Tables of quasinormal frequencies for various parameter configurations are provided based on the sixth-order WKB method. Our findings reveal the differences in the quasinormal modes of black holes in $f(\mathbb{Q})$ gravity compared to those in $f(R)$ and $f(\mathbb{T})$ gravity. This variation demonstrates the impact of different parameter values, offering insights into the characteristics of $f(\mathbb{Q})$ gravity. These results provide the theoretical groundwork for assessing alternative gravities' viability through gravitational wave data, and aid probably in picking out the alternative gravity theory that best aligns with the empirical reality.

gr-qc↗

arXiv2024

Axisymmetric generalization of zero-scalar-curvature solutions from the Schwarzschild metric via the Newman-Janis algorithm

We address a specific issue of the Newman-Janis algorithm: How to determine the general form of the complex transformation for the Schwarzschild metric and ensure that the resulting axisymmetric metric satisfies the zero-scalar-curvature condition, $R=0$. In this context, the zero-scalar-curvature condition acts as a constraint. Owing to this condition, we refer to the class of black holes as the ``Newman-Janis class of Schwarzschild black holes" in order to emphasize Newman-Janis algorithm's potential as a classification tool for axisymmetric black holes. The general complex transformation we derive not only generates the Kerr, Taub-NUT, and Kerr-Taub-NUT black holes under specific choices of parameters but also suggests the existence of additional axisymmetric black holes. Our findings open an alternative avenue using the Newman-Janis algorithm for the construction of new axisymmetric black holes.

gr-qc↗

arXiv2024

Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics

The spectral collocation method (SCM) exhibits a clear superiority in solving ordinary and partial differential equations compared to conventional techniques, such as finite difference and finite element methods. This makes SCM a powerful tool for addressing the Schr\"odinger-like equations with boundary conditions in physics. However, the Chebyshev differential matrix (CDM), commonly used in SCM to replace the differential operator, is not Hermitian but pseudo-Hermitian. This non-Hermiticity subtly affects the pseudospectra and leads to a loss of completeness in the eigenstates. Consequently, several issues arise with these eigenstates. In this paper, we revisit the non-Hermitian Liouville quantum mechanics by emphasizing the pseudo-Hermiticity of the CDM and explore its expanded models. Furthermore, we demonstrate that the spectral instability can be influenced by the compactification parameter.

quant-ph↗

arXiv2023

Phase diagrams of quasinormal frequencies for Schwarzschild, Kerr, and Taub-NUT black holes

The Newman-Janis algorithm, which involves complex-coordinate transformations, establishes connections between static and spherically symmetric black holes and rotating and/or axially symmetric ones, such as between Schwarzschild black holes and Kerr black holes, and between Schwarzschild black holes and Taub-NUT black holes. However, the transformations in the two samples are based on different physical mechanisms. The former connection arises from the exponentiation of spin operators, while the latter from a duality operation. In this paper, we mainly investigate how the connections manifest in the dynamics of black holes. Specifically, we focus on studying the correlations of quasinormal frequencies among Schwarzschild, Kerr, and Taub-NUT black holes. This analysis allows us to explore the physics of complex-coordinate transformations in the spectrum of quasinormal frequencies.

gr-qc↗

arXiv2023

A regular black hole as the final state of evolution of a singular black hole

We propose a novel black hole model in which singular and regular black holes are combined as a whole and more precisely singular and regular black holes are regarded as different states of parameter evolution. We refer to them as singular and regular states, respectively. Furthermore, the regular state is depicted by the final state of parameter evolution in the model. We also present the sources that can generate such a black hole spacetime in the framework of $F(R)$ gravity. This theory of modified gravity is adopted because it offers a possible resolution to a tough issue in the thermodynamics of regular black holes, namely the discrepancy between the thermal entropy and Wald entropy. The dynamics and thermodynamics of the novel black hole model are also discussed when a singular state evolves into a regular state during the change of charge or horizon radius from its initial value to its extreme value.

gr-qc↗

arXiv2023

Regular black holes: A short topic review

The essential singularity in Einstein's gravity can be avoidable if the preconditions of Penrose's theorem can be bypassed, i.e., if the strong energy condition is broken in the vicinity of a black hole center. The singularity mentioned here includes two aspects: (i) the divergence of curvature invariants, and (ii) the incompleteness of geodesics. Both aspects are now taken into account in order to determine whether a black hole contains essential singularities. In this sense, black holes without essential singularities are dubbed regular (non-singular) black holes. The regular black holes have some intriguing phenomena that are different from those of singular black holes, and such phenomena have inspired numerous studies. In this review, we summarize the current topics that are associated with regular black holes.

gr-qc↗

arXiv2023

Regular black holes with improved energy conditions and their analogues in fluids

On the premise of the importance of energy conditions for regular black holes, we propose a method to remedy those models that break the dominant energy condition, e.g., the Bardeen and Hayward black holes. We modify the metrics but ensure their regularity at the same time, so that the weak, null, and dominant energy conditions are satisfied, with the exception of the strong energy condition. Likewise, we prove a no-go theorem for conformally related regular black holes, which states that the four energy conditions can never be met in this class of black holes. In order to seek evidences for distinguishing regular black holes from singular black holes, we resort to analogue gravity and regard it as a tool to mimic realistic regular black holes in a fluid. The equations of state for the fluid are solved via an asymptotic analysis associated with a numerical method, which provides a modus operandi for experimental observations, in particular, the conditions under which one can simulate realistic regular black holes in the fluid.

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