arXiv subjects

Zhoujian Cao

Publications and source records attributed to Zhoujian Cao.

At least 19 recordsLinked to original sources

arXiv2026

Large-Eccentricity Asymptotics and Fast Analytic Approximation for Fourier modes of Post-Newtonian Eccentric Waveforms

In this work, we develop analytic asymptotic methods for computing the Fourier modes of gravitational waves from post-Newtonian binary systems in the quasi-Keplerian parametrization in the high eccentricity regime. We also derive the large-eccentricity asymptotic expansion of the eccentricity enhancement function appearing in the tail contributions to the radiation. Furthermore, based on these results, we construct an endpoint-constrained analytic approximation that significantly accelerates the computation of the Fourier modes at large eccentricity. The overall error of this analytic approximation is controlled within $10^{-3}$, and it remains valid for Fourier modes with $p\le200$ and $e\le 0.9$. This approach provides analytic building blocks for modeling frequency-domain gravitational waves from highly eccentric binaries.

gr-qc↗

arXiv2026

Efficient and stable computation of gravitational-wave fluxes from generic Kerr orbits via a unified Heun-function framework

Modeling extreme-mass-ratio inspirals hinges on the accurate and efficient computation of gravitational-wave fluxes from generic Kerr orbits. Conventional frequency-domain techniques are often limited by costly auxiliary parameter searches and numerical instabilities in the strong-field or high-frequency regimes. We address these challenges by reformulating both the angular and radial Teukolsky equations in terms of confluent Heun functions. Employing a hybrid analytic continuation algorithm to compute the connection coefficients eliminates the dependence on auxiliary parameters, directly yielding globally convergent solutions and scattering amplitudes. To resolve the highly oscillatory source integrands for generic orbits, we implement an adaptive bi-power mapping quadrature. Comprehensive benchmarks under standard double-precision arithmetic demonstrate that, for the total radiative flux summed over 168 low-order modes, our method achieves relative errors of order $10^{-11}$, with computational costs typically reduced by factors of 3--13 compared to the state-of-the-art GeneralizedSasakiNakamura. jl and pybhpt packages. Notably, for highly oscillatory high-order modes, our framework achieves a speedup of up to 60 times compared to specialized oscillatory integrators like GeneralizedSasakiNakamura. jl. These demonstrated gains in precision and efficiency establish the framework as a robust tool for strong-field perturbation theory, providing the numerical foundation for high-order self-force calculations and rapid, high-precision waveform generation.

gr-qc↗

arXiv2026

Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals

Extreme mass-ratio inspirals (EMRIs), with their long-lived and highly relativistic orbital evolution, can probe strong-field spacetime geometry and provide an important means to test general relativity. In this work, we investigate EMRI waveforms in a Schwarzschild-like black hole spacetime arising in bumblebee gravity, where Lorentz symmetry breaking (LSB) is characterized by a dimensionless parameter $\ell$. We construct EMRI waveforms within the Augmented Analytic Kludge (AAK) framework using the modified orbital frequencies and fluxes. We find that $\ell$ significantly affects the orbital evolution and thereby modifies the waveform. These modifications grow with increasing $\ell$ and are further enhanced for more eccentric orbits. Furthermore, using Bayesian analysis, we obtain the posterior distributions of EMRI with the parameter $\ell$ included. Our results show that all injected source parameters are recovered within their $1\,σ$ credible intervals. We find that the bumblebee parameter $\ell$ can be constrained with an uncertainty of order $\mathcal{O}(10^{-4})$ by LISA.

gr-qc↗

arXiv2026

Constraining AGN Disk Properties with Gravitational Waves from Inspiraling Stellar-Mass Binary Black Holes in Hierarchical Triple Systems

Space-based gravitational-wave detectors can observe stellar-mass binary black holes (BBHs) long before merger, allowing weak environmental perturbations to accumulate. For binaries embedded in active galactic nucleus (AGN) disks, the local gas density characterizes the environment of the supermassive black hole (SMBH) and compact-object migration. We study whether such signals can constrain this density when a stellar-mass BBH orbits a Kerr SMBH. We evolve the outer orbit with relativistic corrections and gaseous dynamical friction (DF), and construct the detector-frame waveform including BBH inspiral, de Sitter precession, DF phase correction, and moving-source effects. Using Fisher-matrix calculations for sampled systems, we estimate statistical uncertainties and systematic errors. Larger gas densities generally improve the statistical precision of several source and outer-orbit parameters, but also increase systematic errors when DF is omitted. For favorable GW190521-like systems observed by LISA for one year, the disk density can be constrained at the level of $σ_ρ\sim10^{-12}\text{--}10^{-10}\,{\rm g\,cm^{-3}}$. Such constraints would connect BBH merger environments to the gas structure of galactic nuclei and the conditions that support black hole growth. These results indicate that hierarchical BBH inspirals can probe AGN disk environments, provided that gas effects are modeled consistently.

gr-qc↗

arXiv2026

Effective metric for bound state in an effective-one-body theory based on the third-post-Minkowskian approximation

The effective-one-body (EOB) framework, originally formulated within the post-Newtonian (PN) expansion, is central to modeling and interpreting gravitational-wave signals. Recent developments have incorporated the post-Minkowskian (PM) expansion into EOB theory. In this work, we focus on the bound state dynamics in the PM approximation up to the third order and construct the core ingredients of EOB: the effective metric. We examine two correspondence strategies, one based on the radial action variable and the other on the precession angle. We demonstrate that the radial action variable provides a consistent correspondence, which is further verified by the correspondence based on the precession angle. Building on these results, we adopt an isotropic gauge with a Schwarzschild-like parametrization to fix the remaining freedom. Within this parametrization, the effective metric coefficients are determined at 3PM order. Our results provide a consistent effective metric for the bound state dynamics.

gr-qc↗

arXiv2026

Constructing the canonical harmonic coordinates of Kerr metric to the fourth post-Minkowskian order

In this paper we construct the canonical harmonic coordinates of the Kerr metric within the multipolar post-Minkowskian (MPM) formalism to the fourth post-Minkowskian (4PM) order. Based on the well known Geroch--Hansen moments of Kerr metric and Gürsel's theorem, we derive the exact canonical MPM moments $\mathrm{M}_L,\mathrm{S}_L$, which are free of any gauge moments. With these moments, we iteratively compute the gothic metric perturbation $h^{μν}_{\mathrm{can}}$ up to 4PM order and compute the 4PM canonical metric $g_{μν}^{\mathrm{can}}$. The resulting spatial and time components of these metrics are even functions of the spin parameter $a$ while the mixed components are odd. This parity property distinguishes the canonical coordinates from other harmonic coordinates. To contrast this minimal-gauge construction, we also extract the 1PM source moments of the Kerr metric in the Jiang--Lin coordinates. We find that the Jiang--Lin representation possesses non-vanishing gauge moments starting from the 1PM order, whereas in the canonical representation gauge moments vanish to all orders. This comparison highlights the canonical coordinates as the most gauge-pure representation of the Kerr metric in the MPM framework. The complete canonical metric for the Schwarzschild case is also computed to all PM orders. A recent independent construction by Damgaard et al. using momentum-space recursion yields 4PM equivalent results expressed as a power series in $a$, providing a cross-validation of our closed-form 4PM canonical metric. The coordinate transformation linking the canonical Kerr coordinates to previously known harmonic Kerr coordinates remains an open problem.

gr-qc↗

arXiv2026

Taiji Resolving Power for the Transverse Scalar Mode of Gravitational Waves

We investigate how small a co-propagating transverse-scalar component can be resolved by Taiji in an already identified bright tensor chirp. Using a source-tracked tensor-null response, we formulate the problem in terms of the minimum resolvable scalar strain fraction and evaluate it over the sky. For a one-year benchmark chirp with tensor signal-to-noise ratio $ρ_T=1000$, we find that Taiji can rule out transverse-scalar strain fractions $ε_b\gtrsim0.532\%$ at the all-sky median level. The threshold scales as $ε_{b,\min}\proptoρ_T^{-1}$, so brighter tensor events can probe correspondingly smaller scalar fractions. We further find that this sub-percent resolving power remains predictable under small source-parameter mismatches through the associated tensor-leakage structure.

gr-qc↗

arXiv2026

Scale dependence of the effective gravitational constant from functional renormalization group

The general relativity may not be the final theory of gravity. One possible way to look for the gravity theory beyond general relativity is considering variable gravitational constant. Based on the quantum field theory, the gravitational constant as the coupling constant of gravity interaction may change along with the energy scale. Such scale dependent behavior of the gravitational constant can be well described by the functional renormalization group. In the current work, we investigate such behavior systematically. Firstly we find that such behavior is qualitatively independent of interactions such as the electromagnetic interaction included or not. But quantitatively the behavior is governed by two to-be-determined parameters. In general a limit scale may be introduced by the scale dependence of the gravitational constant. If we assume all physical scales are feasible, the two parameters are limited in some special regions. And more we compare the scale dependence behavior to the existing observations. We find the observation results constraint the two parameters strictly.

gr-qc↗

arXiv2026

Using horizon shadows to distinguish a black hole and a white hole

Within theoretical frameworks such as loop quantum gravity, black holes may evolve into white holes through a quantum bounce. This paper uses general relativistic ray-tracing techniques to calculate the ray-traced imaging of accretion disks from the previous cosmic stage during the Kerr black hole and post-bounce Kerr white hole phases. Calculations show that the black hole image presents a crescent emission ring and a central shadow. In contrast, after radiation from the previous universe penetrates the rotating white hole, eccentric and asymmetric nested intensity ring structures form in the synthetic image due to frame-dragging and lensing effects. We analyze the influence of spin parameters, observation inclinations, and accretion disk geometric configurations on the distribution of this nested ring structure using synthetic images and intensity profiles. Building upon this, we introduce polarized ray-tracing calculations for radiation across evolutionary stages. This process results in the polarization image features after the polarization vector is subjected to the gravitational field and spacetime spin dragging during the photon propagation through the white hole horizon and internal spacetime. The spatial rotation patterns and concentric interference fringes in the white hole polarization images exhibit a distinct inter-ring polarization discontinuity. This phenomenon differs from the polarization behavior of black holes. The intensity ring structures and polarization inter-ring discontinuity features provide multi-band and polarimetric interferometry baselines to overcome morphological observational degeneracies. This provides theoretical guidance for future very-long-baseline interferometry (VLBI) to distinguish black holes and white holes.

gr-qc↗

arXiv2026

Solving Hamiltonian Constraint Equation with Physics-Informed Neural Networks

Numerical relativity (NR), solving Einstein equation numerically, plays an important role in source modelling for gravitational wave astronomy. Traditional methods for NR including finite difference method, spectral method and finite element method have been well developed. But newly developed neural network methods for partial differential equations (PDE) have not been well studied yet for NR. We present a Physics-Informed Neural Network (PINN) method to solve the Hamiltonian constraint equation for binary black hole (BBH) initial data in NR. This equation is a highly non-linear elliptic PDE, posing significant challenges for conventional PINN approaches. To overcome these difficulties, we introduce a set of new techniques. We show that our PINN together with these techniques can successfully solve the Hamiltonian constraint equation for generic BBH systems. Validation against the traditional results demonstrates the high accuracy and robustness of our method, revealing the immense potential of constructing a PINN-based initial data solution to all BBH systems for NR.

gr-qc↗

arXiv2026

Constraining Lorentz and parity violations in gravity with multiband gravitational wave observations

This study evaluates the capability of future multi-band observations of gravitational waves emitted from binary black hole coalescences, utilizing joint third-generation ground-based (CE, ET) and space-based (LISA, Taiji, TianQin) detector networks, to constrain parity and Lorentz symmetry violations in the gravitational sector. We model these effects through a parameterized waveform framework that incorporates a set of parameters that quantify potential deviations from general relativity. The frequency-dependence of their effects is described by power-law indices $β$ (i.e., $β_{\bar ν}$, $β_{\bar μ}$, $β_ν$, and $β_μ$). By analyzing events such as a high-signal noise ratio (SNR) "golden event" like GW250114 and a massive binary system like GW231123 (total mass $190-265 M_\odot$) using two networks of ground- and space-based detectors, we demonstrate that multi-band observations can significantly improve the current constraints on Lorentz and parity violations by several order of magnitude, for both high-frequency ($β> 0$) and low-frequency ($β< 0$) modifications. Our Bayesian analysis reveals that while the exceptional SNR of the GW250114-like event yields superior constraints for high-frequency modifications ($β> 0$), the massive nature of GW231123 provides more stringent limits for low-frequency effects ($β< 0$). This work highlights the critical value of future multi-band gravitational wave astronomy for conducting precision tests of general relativity across diverse binary populations.

gr-qc↗

arXiv2026

Constraining Kerr supermassive black hole properties using gravitational waves from inspiraling stellar-mass binary black holes

We study the capability of future space-based gravitational-wave (GW) detectors to constrain supermassive black hole (SMBH) properties through observations of inspiraling stellar-mass binary black holes (BBHs) orbiting them. Focusing on stable hierarchical triple systems, we model the BBH motion in Kerr spacetime and compute the modulated GW signals using the post Newtonian waveform combined with moving-source transformation. Based on the LISA configuration and second-generation time delay interferometry technology, we estimate parameter uncertainties with the Fisher information matrix. Our results show that the outer semimajor axis has the strongest influence on parameter precision, while the SMBH spin and eccentricity mainly affect their own uncertainties. For high-SNR signals, the SMBH mass and orbital parameters can be measured with relative uncertainties on the order of $10^{-5}$, while the spin magnitude and its orientation can be constrained to within a few percentages. Applying the method to an M87*-like system, GW observations provide more precise measurements of the SMBH mass and spin compared with current electromagnetic observations, highlighting the potential of space-based GW astronomy to probe SMBH properties with high accuracy.

gr-qc↗

arXiv2026

Fundamental Physics and Cosmology with TianQin

The exploration of the surrounding world and the universe is an important theme in the legacy of humankind. The detection of gravitational waves is adding a new dimension to this grand effort. What are the fundamental physical laws governing the dynamics of the universe? What is the fundamental composition of the universe? How has the universe evolved in the past and how will it evolve in the future? These are the basic questions that press for answers. The space-based gravitational wave detector TianQin will tune in to gravitational waves in the millihertz frequency range ($10^{-4} \sim 1$ Hz, to be specific), opening a new gravitational wave spectrum window to explore many of the previously hidden sectors of the universe. TianQin will discover many astrophysical systems, populating the universe at different redshifts: some will be of new types that have never been detected before, some will have very high signal-to-noise ratios, and some will have very high parameter estimation precision. The plethora of information collected will bring us to new fronts on which to search for the breaking points of general relativity, the possible violation of established physical laws, the signature of possible new gravitational physics and new fundamental fields, and to improve our knowledge on the expansion history of the universe. In this white paper, we highlight the advances that TianQin can bring to fundamental physics and cosmology.

gr-qc↗

arXiv2026

Enhancing Early Detection and Localization of Gravitational Waves via Eccentricity-Induced Higher Harmonic Modes with 2G Detector Networks

Early detection and localization of gravitational waves (GWs) are essential for identifying electromagnetic (EM) counterparts, playing a key role in multi-messenger astronomy. However, second-generation (2G) ground-based detectors are most sensitive to frequencies of tens to hundreds of hertz, limiting the in-band duration of GW signals to $\mathcal{O}(0.1)$ to several tens of seconds. This constraint hinders early-warning capabilities and early localization. We present the first theoretical study on how eccentricity-induced higher harmonic modes, which enters the detector band significantly earlier than the dominant mode, enhance early detection and localization in a 2G detector network. By decomposing each harmonic mode in the frequency domain and tracking their sequential entry into the detector band, we analyze the evolution of the average signal-to-noise ratios (SNRs) and localization accuracy as functions of time-to-merger. For a GW170817-like BNS, an eccentricity of $e_0=0.4$ at 10 Hz allows the signal to reach SNR 4 and the detection threshold of SNR 8 approximately 12 and 5 minutes before merger, respectively-gains of 4.5 and 1.5 minutes over the circular case. Localization within $1000 \, (100)\,\rm deg^2$ is achievable 5 (1) minutes before merger, improving by 2 minutes (15 seconds). Our results highlight the potential of eccentricity-induced higher harmonics in improving early warnings and localization, particularly for BNS mergers, enhancing the prospects for multi-messenger astronomy.

gr-qc↗

arXiv2026

A Dynamical Equilibrium Linking Nanohertz Stochastic Gravitational Wave Background to Cosmic Structure Formation

The stochastic gravitational wave background (SGWB) is conventionally treated as a passive relic of its astrophysical and cosmological sources, with negligible back-reaction on the matter content of the Universe. Here we show that this assumption needs to be modified once the SGWB and matter are treated as a dynamically coupled non-equilibrium system. Combining linearized general relativity with the fluctuation-dissipation theorem, we derive a generalized Langevin framework that drives the coupled system toward a dynamical equilibrium, which is characterized by a distinctive strain spectrum with a high-frequency cutoff $\mathcal{W}$, and a scale-dependent coupling parameter that screens gravity progressively for the most massive structures. Three findings support this framework. Fitting the equilibrium spectrum to the NANOGrav 15-year dataset yields a Bayes factor of $48\pm 3.8$ over the supermassive black hole binary baseline, achieved entirely within general relativity and the Standard Model. The PTA-calibrated screening mass scale $m_{c}\sim 10^{12}\text{--}10^{14}\,M_{\odot}$ overlaps, with no free cosmological parameter, the $Λ$CDM-derived linear-to-nonlinear transition mass $M_{\rm NL}$ of cosmic structure at $\sim 8\,h^{-1}\,\mathrm{Mpc}$. Most strikingly, promoting this concordance to a structural identification expresses $\mathcal{W}$ entirely in terms of $M_{\rm NL}$, and its inverse acquires a transparent physical reading as a coherence threshold for SGWB-matter coupling. $\mathcal{W}$ is thereby a derived quantity linking nanohertz gravitational-wave observables to the late-time cosmological sector. The framework makes distinctive scale-dependent predictions testable by forthcoming large-scale structure surveys and space-borne gravitational-wave observatories.

astro-ph.CO↗

arXiv2026

Simultaneously search for multi-target Galactic binary gravitational waves

The search for Galactic binary gravitational waves is a critical challenge for future space-based gravitational wave detectors, such as LISA. We propose an innovative approach to simultaneously explore gravitational waves originating from Galactic binaries by developing a new Local Maxima Particle Swarm Optimization (LMPSO) algorithm. This new approach effectively addresses the inaccuracies often associated with signal subtraction contamination, a challenge for traditional iterative subtraction methods, particularly when dealing with low signal-to-noise ratio (SNR) signals (e.g., SNR $<$ 15). We also account for the effects of overlapping signals and degeneracy noise. To demonstrate the effectiveness of our approach, we use residuals from the LISA mock data challenge (LDC1-4), where 10,982 injected sources with SNR $\ge$ 15 have been removed. For the remaining sources with SNR $<$ 15, our method successfully identifies 6,508 signals, yielding a false alarm rate of $\text{FAS}_{0.8} = 36.8\%$. By focusing on a subset of sources-specifically, those with $f > 3$ mHz and those with $f \le 3$ mHz but SNR $\ge 13$-we identify 3,406 signals, with a reduced false alarm rate of $\text{FAS}_{0.8} = 22.5\%$. We further demonstrate that, within the same detection SNR range, our method achieves a comparable or lower $\text{FAS}$ than other existing methods.

gr-qc↗

arXiv2026

Towards Realistic Detection Pipelines of Taiji: New Challenges in Data Analysis and High-Fidelity Simulations of Space-Based Gravitational Wave Antenna

Taiji, a Chinese space-based gravitational wave (GW) detection project, aims to explore the millihertz GW universe with unprecedented sensitivity. By observing astrophysical and cosmological sources, including Galactic binaries, massive black hole binaries, extreme mass-ratio inspirals, and stochastic gravitational wave backgrounds, etc., Taiji is expected to deliver transformative insights into astrophysics, cosmology, and fundamental physics. However, Taiji's data analysis faces unique challenges compared to ground-based detectors like LIGO-Virgo-KAGRA, such as the overlap of numerous signals, extended data durations, more rigorous accuracy requirements for the waveform templates, incompletely characterized noise spectra, non-stationary noises, and various data anomalies. Taking Taiji as a representative example, this paper reviews the data characteristics and data analysis challenges of space-based GW detection, and introduces the second round of Taiji Data Challenge, a collection of simulation datasets designed as a shared platform for resolving these critical issues. This platform distinguishes itself from previous works by the systematic integration of orbital dynamics based on a full drag-free and attitude control simulation, extended noise sources, more complicated and overlapping GW signals, second-generation time-delay interferometry, and the coupling effect of time-varying arm-lengths, etc. Concurrently released is the open-source toolkit Triangle, which offers the capabilities for customized simulation of signals, noises, and other instrumental effects. By taking a step further towards realistic detection, Taiji Data Challenge II and Triangle altogether serve as a new testbed, supporting the development of Taiji's global analysis and end-to-end pipelines, and ultimately bridging the gaps between observation and scientific objectives.

gr-qc↗

arXiv2026

Distance Estimation and Sky Localization of Eccentric Double White Dwarf Binaries from Gravitational Wave Observations inside Globular Clusters

The cosmic distance scale is built on multiple different techniques for estimating distances in space that are often connected and dependent on multiple measurements and assumptions. Double white dwarf binaries (DWDs) are common objects and are expected to produce gravitational wave (GW) signals that can be observed with space-based detectors such as LISA. By analyzing these signals we should be able to estimate the distance and sky location of the source. Previous studies have done this for circular binaries which, while they are abundant, have, in general, weaker signals than eccentric binaries and it is not possible to differentiate whether a circular binary is in the field or in a dense environment such as a globular cluster (GC). In this paper we used eccentric binaries from MOCCA GC simulations, simulated the GW signal from each binary at locations related to GCs in the Milky Way and estimated the precision on the distance and the sky location of the source. We find that distances can be estimated with higher precision than current day methods even with low eccentricity binaries and higher eccentricity further increases this precision. Although the probability of finding a tight and eccentric DWD is far lower than a circular one, we can expect to find at least a few in the dense environments of the Milky Way, such as GCs. These estimations would be independent measurements with high precision to objects inside dense environments, such as GCs inside the Milky Way and the Magellanic Clouds.

astro-ph.HE↗