arXiv subjects

Chen-Kai Qiao

Publications and source records attributed to Chen-Kai Qiao.

At least 19 recordsLinked to original sources

arXiv2026

Collisions of Multiple Black Holes: A Numerical Relativity Study

Numerical relativity has a profound impact on gravitational theory and gravitational wave astronomy. In this work, we present a systematic study of the head-on collisions of multipule black hole systems within the framework of numerical relativity using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation. The numerical simulations of the dynamical evolution of gravitational fields are computed using the AMSS-NCKU code. We report numerical results for black hole collisions in several symmetric and non-symmetric configurations, in which the black holes are initially at rest and are described by Bowen-York type initial data. Our results suggest that black hole systems with perfectly symmetric configurations (e.g., black holes located at the vertices of a regular polygon or a regular polyhedron) impose strong constraints on the emitted gravitational waves, and no gravitational kick arises in these symmetric systems. For regular polygonal configurations, the radiation is dominated by the plus polarization of the $l=2$, $m=0$ mode. For regular polyhedral configurations, all the quadrupole modes with $l=2$ nearly vanish, and gravitational wave amplitudes are strongly suppressed to the order of $10^{-4}$ or below, which is in accordance with an analysis based on the quadrupole approximation. Gravitational radiations from $m \ne 0$ modes become non-negligible only when non-symmetric configurations are encountered. Keywords: Numerical Relativity, Black Holes, Gravitational Waves, N-Body Systems

gr-qc↗

arXiv2026

Investigation of Circular Photon Orbits in Naked Singularity Spacetimes from a Geometric Method

Circular photon orbits play a pivotal role in both gravitational theories and astronomical observations. However, the properties of circular photon orbits in naked singularity spacetimes remain insufficiently explored and deserve in-depth investigation. The present work is dedicated to a comprehensive study of the features of circular photon orbits in naked singularity spacetimes. Notably, a geometric approach is employed to investigate these orbits, in which the framework of optical geometry together with its intrinsic curvatures plays a crucial role. We analyze the existence of circular photon orbits through the intrinsic geodesic curvature, and then examine the numbers of stable and unstable circular orbits, as well as the topological invariant associated with circular photon orbits. By examining various classes of naked singularity spacetimes, we obtain a general conclusion regarding circular photon orbits that holds for the most of spherically symmetric naked singularity spacetimes: the total number of circular photon orbits is an even integer ($\textit{N} = \text{2}\textit{k}$), consisting of $\textit{k}$ stable orbits and $\textit{k}$ unstable orbits in equal proportion. A mathematical proof of this conclusion is also provided in the present work. Furthermore, a comparison with other categories of spacetimes reveals that the conclusions regarding the number of circular photon orbits in naked singularity spacetimes agree with those obtained for compact object spacetimes without naked singularities, indicating that the number of circular photon orbits is primarily governed by the presence of event horizons rather than spacetime singularities. Keywords: Circular Photon Orbit, Naked Singularity Spacetime, Optical Geometry, Geometric Curvatures

gr-qc↗

arXiv2026

Periodic orbits around a magnetically charged black hole in $f(R,T)$ gravity coupled with Euler-Heisenberg electrodynamics

We systematically investigate the zoom-whirl periodic orbits of a small compact object orbiting a magnetically charged black hole in $f(R, T)$ gravity coupled with Euler-Heisenberg nonlinear electrodynamics. We evaluate the impact of the magnetic charge $Q_m$ and the Euler-Heisenberg parameter $a$ on the characteristics of the innermost stable circular orbit (ISCO) and the marginally bound orbit (MBO). Particularly, we focus on the precession parameter q and systematically examine how the magnetic charge and other parameters affect the trajectories of periodic orbits. Using the numerical kludge method, we generate gravitational waveforms for these periodic orbits. The results presented in our work demonstrate that the magnetic charge can significantly modify not only the precession parameter but also the orbital trajectories of the periodic orbits. Moreover, changing the magnetic charge $Q_m$ could cause a significant phase shift in the gravitational waveforms, while other parameters exert a relatively weaker influence on the gravitational waves.

gr-qc↗

arXiv2026

A User-Friendly Python Interface for the Numerical Relativity Code AMSS-NCKU

Numerical relativity has brought about profound and wide-ranging influences on modern astrophysics and gravitational-wave astronomy. In this study, we present a user-friendly Python interface for the numerical relativity code AMSS-NCKU. This interface facilitates the automation of initializing and executing the AMSS-NCKU simulations, as well as the automatic visualization of the output data. The Python interface can significantly reduce the operational complexity of the AMSS-NCKU simulation workflow, lowering the technical barriers for new users. To show the utility of this Python interface, we present two representative examples of numerical relativity simulations (the binary black hole and triple black hole merger processes), obtaining stable numerical results and the expected physical behaviors for black hole systems. Keywords: Numerical Relativity, Gravitational Waves, Black Holes, Python

gr-qc↗

arXiv2026

Periodic orbits and their gravitational waves in EMRIs: supermassive black hole affected by galactic dark matter halos

Periodic orbits exhibiting zoom-whirl behavior have become attractive topics for studying particle dynamics and gravitational wave emission in extreme-mass-ratio inspirals (EMRIs). This study systematically investigates periodic orbits around black holes and their gravitational wave radiation in three dark matter halo environments: NFW, Beta, and Moore models. The dark matter distribution in these models can be effectively incorporated using two parameters -- the dark matter characteristic mass and halo characteristic radius. Our results reveal that for a larger dark matter mass and a smaller characteristic radius, the shapes of the periodic orbits and the corresponding gravitational waveforms show more significant deviations from the Schwarzschild case. As the halo characteristic radius increases, the orbital shapes and waveform characteristics gradually converge with the Schwarzschild black hole results. Our results also suggest that the NFW and Beta models produce nearly indistinguishable results, while the Moore model shows distinct signatures compared with Beta/NFW models. Furthermore, calculations of characteristic strains in frequency spectra show that gravitational-wave signals associated with these periodic orbits lie above the sensitivity curves of LISA, TianQin, and Taiji, indicating their detectability in future space-based gravitational wave observatories. These findings deepen our understanding of dark matter halo effects on periodic motions and gravitational wave signatures. Keywords: GR black holes; Gravitational waves in GR and beyond: theory; dark matter theory; astrophysical black holes

gr-qc↗

arXiv2026

Orbital Dynamics and Gravitational Wave Signatures of Extreme Mass Ratio Inspirals in Galactic Dark Matter Halos

In astrophysics, extreme mass ratio inspiral (EMRI) systems, which consist of a central supermassive black hole and a stellar-mass compact object (SCO), are typically embedded in galactic dark matter (DM) halos. This dark matter environment inevitably affects the orbital dynamics of the SCO and the gravitational wave (GW) signals emitted by the system. In this work, we select two typical dark matter halo profiles -- the Navarro-Frenk-White (NFW) and Beta models -- to systematically investigate their specific impacts on the long-term orbital evolution of the SCO. By incorporating three dissipative mechanisms -- dynamical friction, accretion, and gravitational radiation reaction -- our results demonstrate that, compared to a pure vacuum medium, the presence of a dark matter halo significantly alters the trajectories of precessing orbits, the dynamical evolution of orbital parameters, and the waveforms and phases of the emitted gravitational waves. Due to the strong accretion effect within the NFW model, the energy flux exhibits a distinctive "cusp" feature, marking a reversal from net energy loss to gain at a specific semi-latus rectum, which is a phenomenon absent in the Beta model. Although short-term observations may not be sufficient to distinguish between the NFW and Beta models, their differences become evident over long-term orbital evolution. The gravitational waveforms computed using the NFW and Beta models exhibit a phase shift, which could be detectable in high-density DM environments. This phase shift becomes even more pronounced for higher eccentric orbits and longer observation times. These results offer a theoretical framework for probing environmental effects on EMRIs across different dark matter models using future space-based gravitational wave observatories.

gr-qc↗

arXiv2026

A General Discussion on Photon Spheres in Different Categories of Spacetimes

Photon spheres have attracted considerable interest in the studies of black holes and other astrophysical objects. For different categories of spacetimes (or gravitational sources), the existence of photon spheres and their distributions are dramatically influenced by the geometric and topological properties of spacetimes and characteristics of the corresponding gravitational fields. In this work, we carry out a geometric analysis on photon spheres for different categories of spacetime (including black hole spacetime, ultra-compact object's spacetime, regular spacetime, and naked singularity spacetime). Some universal properties and conclusions are obtained for these spacetimes. We mostly focus on the existence of photon spheres, the total number of photon spheres $n = n_{\text{stable}} + n_{\text{unstable}}$, the subtraction of stable photon sphere and unstable photon sphere $w = n_{\text{stable}} - n_{\text{unstable}}$ in different categories of spacetimes. These conclusions are derived solely from geometric properties of optical geometry of spacetimes, irrelevant to the specific spacetime metric forms. Besides, our results successfully recover some important theorems on photon spheres proposed in recent years.

gr-qc↗

arXiv2025

Gravitational Lensing of Euler-Heisenberg Black Hole Surrounded by Perfect Fluid Dark Matter

In this work, we study the gravitational lensing of Euler-Heisenberg black hole surrounded by perfect fluid dark matter. This kind of black hole solution enables us to investigate the nontrivial interplay between the dark matter effects and nonlinear electrodynamics effects (or quantum electrodynamics effects) on charged black hole systems. The important observables in gravitational lensings are calculated and discussed in our work, including the gravitational deflection angle of light and time delay of light. Additionally, we also explore the massive orbit's bound orbits (and their precession angles) and black hole shadow radius for Euler-Heisenberg black hole in the presence of dark matter. The results indicate that the Euler-Heisenberg black hole with a larger perfect fluid dark matter parameter could greatly reduce the gravitational deflection angle of light, time delay of light, and precession angle of massive object's bound orbit, while the nonlinear electrodynamics effects do not have large influences on these observables. Keywords: Euler Heisenberg Black Hole; Gravitational Lensing; Perfect Fluid Dark Matter; Nonlinear Electrodynamics

gr-qc↗

arXiv2025

The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Photon sphere has attracted significant attention since the capture of black hole shadow images by Event Horizon Telescope. Recently, a number of studies have highlighted that the number of photon spheres and their distributions near black holes are strongly constrained by black hole properties. Specifically, for black holes with event horizons and proper asymptotic behaviors, the number of stable and unstable photon spheres satisfies the relation $n_{\text{stable}} - n_{\text{unstable}} = -1$. In this study, we provide a new proof on this relation using a geometric analysis, which is carried out using intrinsic curvatures in the optical geometry of black hole spacetimes. Firstly, we demonstrate the existence of photon spheres near black holes assuming most general asymptotic behaviors (asymptotically flat black holes, asymptotically de-Sitter and anti-de-Sitter black holes). Subsequently, we prove that the stable and unstable photon spheres near black holes must be one-to-one alternatively separated from each other, such that each unstable photon sphere is sandwiched between two stable photon spheres (and each stable photon sphere is sandwiched between two unstable photon spheres). Our analysis is applicable to any spherically symmetric black hole spacetimes.

gr-qc↗

arXiv2024

Geometric Approach to Circular Photon Orbits and Black Hole Shadows

Circular photon orbit and black hole shadow are significantly important issues in physics and astronomy, and a number of breakthroughs have been witnessed in recent years. Conventionally, the stable and unstable circular photon orbits are obtained using the effective potential of test particles moving in black hole spacetime. In this work, a pure geometric approach is developed to calculate these circular photon orbits and black hole shadow radius. Furthermore, it can be proved that our geometric approach is completely equivalent to the conventional approach based on effective potentials of test particles.

gr-qc↗

arXiv2024

Gravitational Lensing of Spherically Symmetric Black Holes in Dark Matter Halos

The gravitational lensing of supermassive black holes surrounded by dark matter halo has attracted a great number of interests in recent years. However, many studies employed simplified dark matter density models, which makes it very hard to give a precise prediction on the dark matter effects in real astrophysical galaxies. In this work, to more accurately describe the distribution of dark matter in real astrophysical galaxies, we study the gravitational lensing of black holes in astrophysical dark matter halo models (Beta, Burkert, Brownstein, and Moore). The deflection angle is obtained using a generalized Gibbons-Werner approach. The visual angular positions and the Einstein rings are also calculated by adopting the gravitational lens equation. Specifically, we choose the supermassive black holes in Milky Way Galaxy, Andromeda galaxy (M31), Virgo galaxy (M87), and ESO138-G014 galaxy as examples, including the corresponding fitted value of dark matter halos. The results suggest that the dark matter halo described by the Beta model has non-negligible influences on the gravitational deflection angle and gravitational lensing observations. However, the Burkert, Brownstein, and Moore models have relatively small influences on angular position of images and the Einstein ring.

gr-qc↗

arXiv2024

Time Delay of Light in the Gravitational lensing of Supermassive Black Holes in Dark Matter Halos

The dark matter halo has non-negligible effects on the gravitational lensing of supermassive black hole in the galaxy center. Our work presents a study on the time-delay of light in gravitational lensing of black holes enclosed by dark matter halos. To provide a precise description on the distribution of dark matter in galaxies, we choose several famous phenomenological dark matter halo models in astrophysics, including the NFW, Beta, Burkert and Moore models, to carry out the present study. Through numerically calculating the time-delay of light in gravitational lensing, a comparative analysis of the dark matter effects within different halo models has been performed. Assuming typical length scales associated with the galactic gravitational lensing, numerical results indicate that the NFW, Beta, Burkert and Moore dark matter halos can significantly enhance the time delay of light in gravitational lenisng of central supermassive black holes. The enhancing effect becomes more pronounced with a small dark matter halo scale and an increasing dark matter halo mass. Keywords: Black Hole; Gravitational Lensing; Time Delay; Dark Matter Halo

gr-qc↗

arXiv2023

Gravitational Lensing of Schwarzschild and Charged Black Holes Immersed in Perfect Fluid Dark Matter Halo

Dark matter and dark energy dominate the behavior of our universe. The dark matter usually forms halo structures in large number of galaxies. Properties of dark matter halo can be revealed and understood from the gravitational lensing observations. In this work, a comprehensive study on the gravitational lensing of black holes immersed in dark matter halos is presented. To effectively model the supermassive black hole in a galaxy center (which is surrounded by dark matter halo) in a simple way, we investigate the Schwarzschild black hole and charged Reissner-Nordström black hole immersed in a perfect fluid dark matter halo. In the present work, several basic quantities in gravitational lensing (the gravitational deflection angle of light, photon sphere, black hole shadow radius, gravitational lens equation and Einstein ring) are calculated and analyzed analytically and numerically. A second order analytical expansion of gravitational deflection angle is obtained in the weak deflection limit, and the full gravitational deflection angle (including all order perturbation contributions applicable to both weak and strong deflection limits) is also calculated numerically as comparisons. It enables us to analyze the perfect fluid dark matter influences on gravitational deflection angle and gravitational lensing beyond the leading order, which were not sufficiently studied in previous works. Assuming $M \sim λ_{\text{DM}} \sim Q$, our results show that dark matter can greatly influence the gravitational lensing of central black holes.

gr-qc↗

arXiv2023

The Gravitational Bending of Acoustic Schwarzschild Black Hole

Acoustic black hole is becoming an attractive topic in recent years, for it open-up new direction for experimental / observational explorations of black holes. In this work, the gravitational bending of acoustic Schwarzschild black hole is investigated. The gravitational deflection angle of particles traveling along null geodesics, weak gravitational lensing and Einstein ring for acoustic Schwarzschild black hole are carefully studied and analyzed. Particularly, in the calculation of gravitational deflection angle, we resort to two approaches -- the Gauss-Bonnet theorem and the geodesic method. The results show that the gravitational bending effect in acoustic Schwarzschild black hole is enhanced, compared with conventional Schwarzschild black hole. This result indicates that the acoustic black holes may be more easily detectable in gravitational bending effects and weak gravitational lensing observations.

gr-qc↗

arXiv2022

Curvatures, Photon Spheres and Black Hole Shadows

In a recent work PRD 106, L021501 (2022), a new geometric approach is proposed to obtain the photon sphere (circular photon orbit) and the black hole shadow radius. In this approach, photon spheres and the black hole shadow radius are determined using geodesic curvature and Gaussian curvature in the optical geometry of black hole spacetimes. However, the calculations in PRD 106, L021501 (2022) only restricted to a subclass of static and spherically symmetric black holes with spacetime metric $g_{tt} \cdot g_{rr}=-1$, $g_{θθ}=r^{2}$ and $g_{ϕϕ}=r^{2}\sin^{2}θ$. In this work, we extend this approach to more general spherically symmetric black holes (with spacetime metric $ds^{2}=g_{tt}dt^{2}+g_{rr}dr^{2}+g_{θθ}dθ^{2}+g_{ϕϕ}dϕ^{2}$). Furthermore, it can be proved that our results from the geometric approach are completely equivalent to those from conventional approach based on effective potentials of test particles.

gr-qc↗

arXiv2021

An Overview of the Compton Scattering Calculation

The Compton scattering process plays significant roles in atomic and molecular physics, condensed matter physics, nuclear physics and material science. It could provide useful information on the electromagnetic interaction between light and matter. Several aspects of many-body physics, such us electronic structures, electron momentum distributions, many-body interactions of bound electrons, \emph{etc}, can be revealed by Compton scattering experiments. In this work, we give a review on \emph{ab initio} calculation of Compton scattering process. Several approaches, including the free electron approximation (FEA), impulse approximation (IA), incoherent scattering function / incoherent scattering factor (ISF) and scattering matrix (SM) are focused in this work. The main features and available ranges for these approaches are discussed. Furthermore, we also briefly introduce the databases and applications for Compton scattering.

cond-mat.other↗

arXiv2021

Relativistic Impulse Approximation in the Atomic Ionization Process induced by Millicharged Particles

The millicharged particle has become an attractive topic to probe physics beyond the Standard Model. In direct detection experiments, the parameter space of millicharged particles can be constrained from the atomic ionization process. In this work, we develop the relativistic impulse approximation (RIA) approach, which can duel with atomic many-body effects effectively, in the atomic ionization process induced by millicharged particles. The formulation of RIA in the atomic ionization induced by millicharged particles is derived, and the numerical calculations are obtained and compared with those from free electron approximation and equivalent photon approximation. Concretely, the atomic ionizations induced by mllicharged dark matter particles and millicharged neutrinos in high-purity germanium (HPGe) and liquid xenon (LXe) detectors are carefully studied in this work. The differential cross sections, reaction event rates in HPGe and LXe detectors, and detecting sensitivities on dark matter particle and neutrino millicharge in next-generation HPGe and LXe based experiments are estimated and calculated to give a comprehensive study. Our results suggested that the next-generation experiments would improve 2-3 orders of magnitude on dark matter particle millicharge $δ_χ$ than the current best experimental bounds in direct detection experiments. Furthermore, the next-generation experiments would also improve 2-3 times on neutrino millicharge $δ_ν$ than the current experimental bounds.

hep-ph↗

arXiv2020

Compton Scattering Energy Spectrum for Si and Ge Systems

In the present work, we study the atomic Compton Scattering which could have great impacts on dark matter direct detection experiments. We give a quantitative analysis of the Compton scattering energy spectrum for Si and Ge atomic systems. The theoretical results on Compton scattering are calculated within the frameworks of free electron approximation (FEA) and relativistic impulse approximation (RIA). The low-energy transfer and near photoionization threshold regions are especially considered in this work. In RIA calculation, to obtain the atomic ground states, we adopt an \emph{ab initio} calculation in the fully relativistic Dirac-Fock theory.

physics.atom-ph↗