arXiv subjects

Kai Lin

Publications and source records attributed to Kai Lin.

At least 19 recordsLinked to original sources

arXiv2026

Coherent multipath wave response on Reissner-Nordstr\"{o}m analogue surface

To uncover how the intrinsic metric of a relativistic compact object governs macroscopic wave phenomena, we establish a theoretical framework mapping the charge dependent spatial geometry of a Reissner-Nordstr\"{o}m (RN) black hole onto the coherent response of an analogue curved surface. By solving an exact spatial geodesic boundary value problem on an isometrically embedded equatorial slice, we extract the discrete multi-loop path-length spectrum and convert this geometric backbone into a physical wave field via a finite-path surface Huygens-Fresnel construction. We analytically compute the arbitrary order winding trajectories alongside their high winding accumulation limits, demonstrating that the analogue charge acts as a precise physical dial that reconfigures the event horizon throat and fundamentally reorganizes the discrete path sequence. Furthermore, we find that this underlying geometric deformation uniquely dictates the macroscopic interference, revealing that steady state spatial fringes, spectral resonance combs, and transient temporal echo ladders are intrinsically unified physical projections of a single charge controlled path spectrum. This systematic parameter to response methodology establishes a rigorous theoretical bridge between strong field gravitational lensing and tabletop transformation optics, providing a highly tunable blueprint for future multi domain analogue gravity experiments.

gr-qc↗

arXiv2026

Stationary Dirac condensates around Kerr black holes

Ultralight bosonic fields can form macroscopic clouds around rotating black holes, whereas the existence of analogous stationary fermionic condensates is strictly constrained by their intrinsic spin. Here we establish a complete geometric and kinematic framework to resolve the stationary bound states of massive Dirac fields on Kerr and Kerr-Newman backgrounds. By mapping the Kerr-Dirac system to a globally integrated sourced radial problem, we strictly isolate the boundary constraints dictated by horizon causality. The angular sector reveals a fundamental topological distinction: because the azimuthal quantum number is strictly half-integer, the regular boundary branches prevent the local field density from vanishing on the rotation axis. Consequently, rotating fermionic clouds inherently form globally filled, oblate geometries, in stark contrast to the hollow toroidal structures characteristic of scalar condensates. Crucially, our radial indicial analysis unveils the exact mathematical origin of the absence of synchronized Dirac hair. Precisely at the kinematic synchronization locus, the Frobenius matrix of the Dirac operator is non-defective and entirely devoid of logarithmic divergences. Without these singular branches to be selectively excised by boundary regularity, the physical burden of existence falls entirely onto the causal flux barrier, which strictly trivializes the zero-source amplitude. This synchronization veto demonstrates that a black hole's capacity to support macroscopic stationary fields is governed not merely by superradiant kinematics, but by the profound interplay between local horizon causality and quantum spin statistics.

gr-qc↗

arXiv2026

Optical Images of the Braneworld Black Hole Surrounded by an Optically Thin Accretion Disk

This work examines the observational signatures of rotating black holes with tidal charge in the Randall--Sundrum braneworld scenario. Combining an elliptic-integral-based analytical treatment with numerical ray tracing, we characterize photon motion around braneworld black holes in detail. For small observer inclinations, secondary images remain embedded inside the primary emission rings. As the inclination becomes larger, the primary and secondary images gradually separate and produce a strongly asymmetric image morphology. We show that the image asymmetry and the deformation of the inner shadow are jointly controlled by the black hole spin, the tidal charge, and the observer inclination. To analyze the frequency shifts across the accretion disk, we extend the emitting region from the ISCO down to the event horizon by including the plunging flow. The results indicate that the observer inclination is the dominant factor governing the frequency-shift distribution. In addition, we reconstruct braneworld black hole images using a fisheye-lens ray-tracing model. The optical morphology and brightness distribution show a clear dependence on the observing frequency, especially when comparing 230~GHz with 86~GHz. We also contrast the brightness distributions of prograde and retrograde disks, finding that both the total intensity and the peak intensity at 86~GHz are higher than those at 230~GHz. For negative values of the tidal charge, we further investigate the corresponding frequency-shift behavior and 230~GHz intensity profiles, which may provide useful theoretical guidance for future studies of extra-dimensional gravity models.

astro-ph.HE↗

arXiv2026

Optical Appearances of Accreting Ellis-Bronnikov Wormholes Observed from Both Sides of Throats

This study investigates the optical appearance of the Ellis-Bronnikov wormhole as viewed from both sides of its throat, under conditions of optically thick and thin accretion. By solving the geodesic equation, we derive the relationship between the impact parameter and the aiming distance of photons, and found that if the observer and the accretion disk are located on both sides of the throat, these two quantities are not equal. The optical image of the wormhole observed from the other side of the throat is obtained through the ray-tracing method. For optically thick accretion, increases in the parameter $n$ lead to an increase in the apparent size of the wormhole but a decrease in its brightness. For optically thin accretion, the image is similar to the internal and external inversion of the image observed from the other side. Furthermore, for optically thin accretion flows, the direct image does not block the emission from higher-order images, allowing radiation emitted from regions much closer to the event horizon to reach the observer. Our simulation results show that when the observer is on the $\mathcal{R}^+$ side, EB wormholes with small $n$ can mimic the images taken by the EHT to some extent, while wormholes with large $n$ or with the observer on the $\mathcal{R}^-$ side can be ruled out.

gr-qc↗

arXiv2026

Gravitational waveforms from periodic orbits around Gauss-Bonnet black holes

Extreme mass-ratio inspirals (EMRIs) constitute one of the most promising probes of strong field gravity for future space borne gravitational-wave observatories. As a representative higher-curvature extension of General Relativity (GR), four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity is distinguished by its strictly linear geometric coupling. By this mathematical property, the pathological Fisher-matrix singularities that typically plague conventional modified black hole models are effectively evaded, thereby providing an ideal framework to test topological deviations from classical spacetimes. Through the classification of equatorial periodic orbits via an integer taxonomy $(z,w,v)$, it is demonstrated that even modest Gauss-Bonnet couplings ($\alpha \sim 0.1M^2$) imprint measurable geometric signatures onto the zoom-whirl architecture. Although the global conservative energy budget is shifted by a mere $\sim 0.2\%$, the short-range repulsive EGB core severely alters the strong field whirl dynamics, whereby a resolvable macroscopic dephasing of several radians per orbit is accumulated. Through semi-relativistic waveform modeling, it is revealed that this temporal compression manifests as a rigid, high-frequency stretching of the gravitational-wave harmonic comb -- a clean, amplitude-independent spectral signature ideally suited for detection by LISA, Taiji, and TianQin. A rigorous Fisher information analysis confirms that for a typical four-year observation at a signal-to-noise ratio of $\rho=20$, the marginalized error on the EGB coupling can be tightly bounded to $\sigma_\alpha \sim \mathcal{O}(10^{-6}) M^2$, with virtually negligible parameter degeneracy with the orbital eccentricity.

gr-qc↗

arXiv2026

Polarization Signatures of Rotating Black Holes in Perfect Fluid Dark Matter Spacetimes

Motivated by horizon-scale polarization observations of M87^{*}, we investigate polarized emission from rotating black holes (BHs) immersed in a perfect fluid dark matter (PFDM) background. Fully relativistic ray tracing is utilized to examine how the polarization structure jointly depends on magnetic-field geometry, higher-order imaging, and the PFDM intensity parameter k. We show that, for a given k value, magnetic configurations with a polar component naturally produce a continuous spiral pattern in the electric vector position angle (EVPA), while the large-scale EVPA morphology remains primarily controlled by the magnetic-field topology. Variations in k affect light propagation and polarization transport near the horizon, leading to corresponding changes in EVPA deflection and polarized intensity around the photon ring. A decomposition of the total polarized image further reveals that higher-order images provide localized yet non-negligible corrections near the ring. Compared with the polarization characteristics of M87^{*} inferred by the EHT, image-domain quantities such as |m|_{\rm net} and \arg\beta_2 indicate that PFDM induces systematic shifts relative to the pure Kerr BH case, lowering the net linear polarization fraction and modifying the large-scale polarization phase. Overall, PFDM acts as an additional strong-gravity ingredient that systematically reorganizes the horizon-scale polarization structure, suggesting that surrounding dark matter can leave observable imprints on black hole polarization signatures.

astro-ph.HE↗

arXiv2026

UFO-DETR: Frequency-Guided End-to-End Detector for UAV Tiny Objects

Small target detection in UAV imagery faces significant challenges such as scale variations, dense distribution, and the dominance of small targets. Existing algorithms rely on manually designed components, and general-purpose detectors are not optimized for UAV images, making it difficult to balance accuracy and complexity. To address these challenges, this paper proposes an end-to-end object detection framework, UFO-DETR, which integrates an LSKNet-based backbone network to optimize the receptive field and reduce the number of parameters. By combining the DAttention and AIFI modules, the model flexibly models multi-scale spatial relationships, improving multi-scale target detection performance. Additionally, the DynFreq-C3 module is proposed to enhance small target detection capability through cross-space frequency feature enhancement. Experimental results show that, compared to RT-DETR-L, the proposed method offers significant advantages in both detection performance and computational efficiency, providing an efficient solution for UAV edge computing.

cs.CV↗

arXiv2026

What does a regular star look like?

Recently, astronomers discovered unusual Einstein cross images of the galaxy HerS-3, which feature a bright central spot. Motivated by studies of images produced by regular stars, it has been proposed that optical appearances caused by compact stars acting as gravitational lenses may account for this central bright spot. We further suggest that images produced by regular stars exhibit additional characteristics distinct from those of ordinary black holes, such as the possible partial or complete absence of secondary images. These phenomena may serve as favorable observational criteria for identifying regular stars in future searches.

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 P\"oschl-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

Polarized Radiative Transfer of Kerr-Newman Black Hole

In this analysis, we investigate the polarization radiation imaging of Kerr-Newman black holes, with a particular focus on the impact of black hole charge on photon propagation and polarization characteristics. By extending the traditional Walker-Penrose method, which is limited by its reliance on specific symmetric structures and Killing tensors, we overcome these limitations by constructing an ordinary differential equations (ODEs) numerical framework that combines the photon orbit equation with the polarization parallel transport equation. This allows for the self-consistent evolution of photon trajectories and polarization states in any spacetime backgrounds without relying on specific symmetries. Using this framework, we analyze the effects of black hole spin and charge on the polarization characteristics of radiation from both prograde and retrograde accretion disks. Our results show that black hole charge can significantly modify photon trajectories and polarization patterns: increasing charge compresses and distorts the EVPA structure on photon-ring scales, inducing localized rotations and asymmetries that may provide a potential diagnostic of a nonzero black hole charge.

gr-qc↗

arXiv2025

Universality in quasinormal modes of a magnetized black hole

In this work, we investigate the linear stability of a magnetized Einstein-Maxwell solution describing a static, axially symmetric black hole (BH) immersed in a uniform magnetic field $B$. We probe the dynamics of an external charged scalar field through its quasinormal modes (QNMs), combining frequency- and time-domain analyses. We find a critical value of the field charge at which the QNM spectrum exhibits universal power-law scaling with an exponent of approximately $1/2$. This critical behavior admits a simple interpretation in terms of a transition between a confined regime, where waves remain effectively trapped within a region of characteristic size $\sim 1/B$, and a deconfined regime, where the field reaches distances $\gg 1/B$ and the damping rate becomes parametrically small. These results provide qualitative and quantitative insights that may inform more realistic scenarios involving highly magnetized compact objects.

gr-qc↗

arXiv2025

Axial Gravitational Normal Modes of Uniform Density Star in Anti-de Sitter Spacetime

The article studies the dynamical behavior of axial gravitational perturbations of homogeneous stars in Anti-de Sitter spacetime. Because the radial coordinate $r$ transforms into the tortoise coordinate $y = y(r)$, obeying $y(r=0)=0$ and $y(r\rightarrow\infty)=y_\text{max}<\infty$, the tortoise coordinates domain is finite, and the gravitational waves fail to reach out of the domain. Thus, from the perspective of tortoise coordinates, the perturbation equation of uniform density stars in Anti-de Sitter spacetime is analogous to the infinite deep potential well in quantum mechanics. Therefore, the perturbative behavior in this spacetime represents a standing wave vibration. Here we use shooting method and finite difference method to show the imagery of standing waves in this spacetime for $n=0,1,2$ as examples. On the other hand, by finite difference method, a Gaussian wave packet bounces back and forth within this potential well. Furthermore, due to the shape of the gravitational potential function $V$ within the range $0\le y\le y_\text{max}$, an echo phenomenon occurs at the surface of the star. As the energy of the wave packet remains within the potential well, each time it traverses the surface of the star, a reflective echo is generated. Consequently, after multiple reflections, the Gaussian wave packet cannot maintain its original shape and ultimately disperses.

gr-qc↗

arXiv2025

Stretchable and self-adhesive triboelectric sensor for real-time musculoskeletal monitoring and personalized recovery

Recent advances in medical diagnostics have highlighted the importance of wearable technologies for continuous and real-time physiological monitoring. In this study, we introduce a flexible, self-powered triboelectric nanogenerator (MB-TENG) engineered from commercially available medical elastic bandages for biomechanical sensing during rehabilitation and gait analysis. Leveraging the porous and skin-friendly properties of the bandage combined with a PTFE film, the MB-TENG delivers robust electrical performance, achieving a peak open-circuit voltage (VOC) of 122~V, a short-circuit current (ISC) of 25~$\mu$A, and a transferred charge (QSC) of 110~nC, while maintaining long-term stability across 40{,}000 mechanical cycles. Its inherent self-adhesive property allows for multi-layer assembly without extra bonding agents, and mechanical stretching enhances output, enabling dual configurability. A stacked design further improves the power capacity, supporting applications in wearable medical electronics. The MB-TENG device seamlessly conforms to joint surfaces and foot regions, providing accurate detection of motion states and abnormal gait patterns. These features underscore the MB-TENG's potential as a low-cost, scalable platform for personalized rehabilitation, injury monitoring, and early musculoskeletal diagnosis.

physics.med-ph↗

arXiv2025

Image of a time-dependent rotating regular black hole

In this study, we develop a modeling framework based on spatio-temporal generalized random fields to simulate the time-evolving accretion flows and their associated imaging signatures around rotating regular black holes. We extend the Mat\'ern field formalism to the spatio-temporal domain and introduce a locally anisotropic tensor structure $\Lambda(\mathbf{x})$, which encodes direction-dependent correlation scales motivated by Keplerian velocity fields, thereby generating physically informed perturbation structures. Coupled with a computationally efficient light ray-tracing scheme, this framework produces a sequence of time-resolved images of regular black hole shadow and accretion structures. By incorporating light-travel time effects, we identify significant temporal smearing of features within strongly lensed regions and rapidly varying sources, thus enhancing the physical realism of the modeling. Comparison with existing general relativistic magnetohydrodynamic simulations demonstrates that our stochastic generative model maintains statistical consistency while offering substantial computational efficiency. Moreover, the simulated results reproduce the dynamic positional shift of the bright ring structure observed in M87$^{*}$, providing theoretical support for interpreting its time-variable images.

astro-ph.HE↗

arXiv2025

Echoes of bimodal axial gravitational perturbations in a uniform-density star in Einstein-{\AE}ther gravity

This paper studies axial gravitational perturbations of a uniform-density star in scalar-Einstein-{\AE}ther 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 {\AE}ther 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-{\AE}ther. We present numerical calculations and discuss the potential implications of our findings.

gr-qc↗

arXiv2025

Image of the time-dependent black hole

The Event Horizon Telescope's 2024 observations report a shift in the position angle of the brightness asymmetry in M87*, revealing time variability in the black hole's image. In this analysis, we investigate the time-dependent of a Vaidya black hole. By introducing a mass function that increases linearly with time, along with a conformal transformation, we derive the conformal Vaidya metric and define a new time coordinate $t_c$. Using the semi-analytical approach, we analyze the ray trajectories and radiation flux of the Vaidya black hole in the background of a thin accretion disk. We discuss how the observed flux in the Vaidya spacetime evolves as a function of the new time coordinate $t_c$. The results show that the facula on the observable plane undergoes radial displacement as $t_c$ increases, revealing the time-dependent evolution of black hole images.

gr-qc↗

arXiv2025

The constraints on the stochastic gravitational wave background from cosmic strings by an electromagnetic resonance system

As one of the primary detection targets for contemporary gravitational wave (GW) observatories, the stochastic gravitational wave background (SGWB) holds significant potential for enhancing our understanding of the early universe's formation and evolution. Studies indicate that the SGWB spectrum from cosmic strings can span an extraordinarily broad frequency range, extending from extremely low frequencies up to the microwave band. This work specifically investigates the detectability of cosmic string SGWB signals in an electromagnetic (EM) resonance system at GHz frequency. We present a systematic analysis encompassing: (1) the response of high frequency gravitational waves (HFGWs) in such EM resonance system. (2) the development and application of fundamental data processing protocols in the EM resonance system. Our results demonstrate that the EM system shows promising sensitivity to detect cosmic string SGWB signals with tension parameters $G\mu\geq 10^{-11}$ (the corresponding dimensionless amplitude $h \geq 10^{-33}$ at 1 GHz), while potentially establishing new constraints for $G\mu\leq 10^{-11}$ in the microwave band. These findings would complement existing multi-band SGWB observations and provide additional constraints on cosmic-string tension parameters in GHz frequency regimes.

gr-qc↗

arXiv2025

Gravitational wave cosmology in Einstein-scalar-Gauss-Bonnet gravity

In the framework of Einstein-scalar-Gauss-Bonnet (EsGB) gravity, we systematically study gravitational waves (GWs), first produced by remote compact astrophysical sources and then propagating through the flat homogeneous and isotropic Universe at cosmic distances before arriving at detectors. Assuming that the speed $c_T$ of the spin-2 graviton is the same as that of photons, we find explicitly the stability conditions of the theory and then obtain the severest observational constraint found so far. In particular, all these conditions and constraints are satisfied, provided that $0 \leq \alpha\dot{f}(\phi_0) \lesssim 8.97 \times 10^{-24}$ (km), where $\alpha{f}(\phi)$ denotes the coupling strength between the scalar field $\phi$ and the Gauss-Bonnet term, an over-dot represents the derivative with respect to the cosmic time, and $\phi_0$ is the present value of $\phi$. The trajectories for both spin-2 and spin-0 gravitons and the amplitudes of GWs along the trajectories are explicitly obtained. The amplitude of a spin-2 GW is practically indistinguishable from that of GR, while the spin-0 GWs remain almost constant during radiation- and matter-dominated epochs, and in the dark energy-dominated epoch it is proportional to the physical distance between the source and the observer. A careful analysis shows that the latter is due to the assumption $c_T = 1$. When $c_T \not= 1$ to the extent that is consistent with the stability conditions and observational constraints, the above behavior disappears.

gr-qc↗