arXiv subjects

Sizheng Ma

Publications and source records attributed to Sizheng Ma.

At least 19 recordsLinked to original sources

arXiv2026

A nonlinear voice from GW250114 ringdown

Gravitational-wave astronomy, by detecting ripples in spacetime, has opened a new window to observe compact objects and probe theories of gravity in the nonlinear strong-field regime. The ringdown signal of a binary black hole merger contains a superposition of damped sinusoids known as quasi-normal modes (Ref.[1]), whose frequencies are completely determined by the mass and spin of the remnant black hole and form the basis of black hole spectroscopy (Refs.[2-4]). A crucial prediction yet to be observationally confirmed is the existence of quadratic quasi-normal modes, which represent fundamental properties associated with wave-wave coupling in general relativity, and the leading mode is predicted to be detectable with next-generation ground-based detectors (Refs.[5-7]) using traditional methods. Here we show the first observational evidence for a set of quadratic quasi-normal modes in the ringdown of the binary black hole merger GW250114, the loudest gravitational-wave event detected to date, enabled by a novel analysis. These nonlinear modes result from the quadratic coupling of the linear $(2,2,n)$ modes with $n\leq3$. Starting the analysis at a time corresponding to four times the remnant mass ($M_\mathrm{f}$) after the merger, the evidence for their presence reaches a Bayes factor of 62. A phenomenological test allowing these modes to deviate from the theoretical prediction rejects the zero-amplitude hypothesis at a significance of 3.4 $σ$, while the inferred amplitude and complex frequency are consistent with the prediction of general relativity. This finding provides the first observational evidence of gravitational wave-wave interaction and extends black hole spectroscopy from the linear to the nonlinear regime. It also establishes a new direction for testing the fundamental nonlinear structure of general relativity with the most extreme gravity.

gr-qc↗

arXiv2026

Formation of Merging Black Hole Binaries Inside Massive AGN Stars

Stars embedded in the disks of active galactic nuclei (AGN) can grow to hundreds of solar masses, and the same disks are expected to host a population of stellar-mass black holes. A star may therefore capture passing black holes, turning its interior into a potential factory for forming compact binary black hole systems and, ultimately, for the gravitational-wave events seen by our detectors. We test how readily this channel operates using three-dimensional hydrodynamic simulations of black hole--star encounters. As a proof of principle, we adopt a star-to-black-hole mass ratio of $34\!:\!1$, and find that the capture does not disrupt the structure of the star: it heats the star by $10$--$30\%$, and the star loses only $\lesssim1\%$ of its mass throughout. The captured black hole loses its orbital angular momentum rapidly to dynamical friction, sinking to the stellar center within a stellar dynamical time $\lesssim10^{4}\,$s. If the star already harbors a black hole at its center, the two form a bound binary whose gravitational-wave coalescence time falls below $10^{4}\,$yr. Depending on the geometry and speed of the encounter, the resulting orbit may be nearly circular or retain substantial eccentricity. Our calculations confirm that black hole--star encounters in AGN disks are indeed a viable channel for assembling stellar-mass black hole binaries and supplying sources for gravitational-wave detectors.

astro-ph.HE↗

arXiv2026

From driven oscillations to free ringdown: a particle plunging into Kerr

We show that a ringdown waveform can admit a constant-coefficient quasinormal-mode (QNM) representation while its individual QNM-pole contributions remain driven. To establish this result, we construct a first-principles rational approximation to the Kerr Green's function from its QNM poles, physical residues, and horizon-frequency zeros. For particles plunging from the innermost stable circular orbit into Kerr black holes with spins 0.5-0.9, each QNM-pole contribution initially follows the source's instantaneous complex frequency and decouples only after the source decays faster than the corresponding mode. At late times, the source approaches a sum of damped oscillations at the third and higher horizon frequencies. The corresponding zeros in the Green's function cancel these source-frequency components in the coherent waveform, while the continuing drive generates oscillations at QNM frequencies. Thus, an apparently free QNM superposition can emerge before its individual contributions dynamically decouple from the source.

gr-qc↗

arXiv2026

Complex frequency evolution of direct waves from binary black hole mergers

While no signal originating at a black hole's event horizon can reach future null infinity, information about the horizon and its immediate vicinity can be encoded in asymptotic properties of waves emitted by matter or field perturbations falling toward a growing/forming horizon. Within a response-filtered framework, "direct wave" denotes source-sensitive plunge and remnant-formation information revealed by filtering the black-hole response. Unlike a stationary damped sinusoid with a fixed complex frequency, the direct wave follows the evolving source and has an evolving instantaneous complex frequency tied at late times to the remnant horizon angular velocity $Ω_H$ and surface gravity $κ_H$. Using rational filters, we remove quasinormal modes from numerical-relativity waveforms to study this evolution. Before numerical contamination, trajectories depend on remnant spin: the real frequency evolves toward $2Ω_H$ from above for lower spins ($χ_f\lesssim0.7$) and from below for higher spins ($χ_f\gtrsim0.7$), while the instantaneous decay rate increases toward $\sim2κ_H$ and, in some high-spin cases, beyond it. As in particle-plunge results, the horizon-controlled value is approached only at late times, as frame dragging controls near-horizon motion. For $χ_f\sim0.7$ remnants of non-precessing, comparable-mass binaries, the early-time real frequency is close to $2Ω_H$ because the binary orbital frequency transitions smoothly to the remnant horizon frequency. Finite-time deviations therefore carry information about merger/collapse dynamics rather than undermining the horizon connection. Full direct-wave evolution requires numerical-relativity calibration. We further show that approximate pole-zero pairing in the Kerr response motivates a spin-dependent minimal filter set that suppresses quasinormal-mode features while revealing source-trajectory information.

gr-qc↗

arXiv2026

Black hole spectroscopy: from theory to experiment

The "ringdown" radiation emitted by oscillating black holes has great scientific potential. By carefully predicting the frequencies and amplitudes of black hole quasinormal modes and comparing them with gravitational-wave data from compact binary mergers we can advance our understanding of the two-body problem in general relativity, verify the predictions of the theory in the regime of strong and dynamical gravitational fields, and search for physics beyond the Standard Model or new gravitational degrees of freedom. We summarize the state of the art in our understanding of black hole quasinormal modes in general relativity and modified gravity, their excitation, and the modeling of ringdown waveforms. We also review the status of LIGO-Virgo-KAGRA ringdown observations, data analysis techniques, and the bright prospects of the field in the era of LISA and next-generation ground-based gravitational-wave detectors.

gr-qc↗

arXiv2026

Towards long and accurate numerical relativity waveforms of binary black holes beyond general relativity

Numerical relativity (NR) simulations of compact binaries in theories beyond general relativity (GR) will be pivotal for the continued development of future tests of gravity with gravitational waves (GWs). In this Letter, we show that the combination of spectral methods and the "fixing-the-equations" approach allows us to produce the longest waveforms in the literature for a genuine beyond-GR theory, thus bringing NR methods for alternative theories of gravity closer to the state-of-the-art in GR. For concreteness, we focus on the well-known shift-symmetric version of scalar Gauss-Bonnet gravity, a theory postulating the existence of an additional dynamical scalar and describing black holes (BHs) different from the Kerr solution. We extract the gravitational and scalar waveforms at future null infinity for equal-mass, nonspinning, eccentricity-reduced BH binaries, and quantify the phase errors to be $\lesssim$ 1 rad after 40+ GW cycles (20+ orbits). We also show that the GW phase corrections in this alternative theory are distinguishable from Einstein's theory and lead to an earlier coalescence time than in GR. Obtaining such waveforms is a stepping stone to perform precise comparisons with Post-Newtonian theory and to calibrate waveform models beyond GR.

gr-qc↗

arXiv2026

High-accuracy drivers to simulate black hole binaries beyond general relativity with the fixing-the-equations approach

We implement the "fixing-the-equations" approach [Phys.Rev.D 96 (2017) 8, 084043] in spectre, an NR code using a pseudo-spectral discontinuous Galerkin scheme, to produce long and accurate NR waveforms in the well-known shift-symmetric version of scalar Gauss-Bonnet (sGB) gravity. To achieve this, we introduce a new family of comoving driver equations that exploits the approximate symmetries of quasicircular binary systems and is designed to recover the exact (quasi-)stationary solutions of the fully-coupled theory. We validate our single black hole (BH) solutions against analytic predictions and show that, even for binary BHs in the early inspiral, the intrinsic BH quantities are relatively insensitive to the timescales entering the driver equation. Attention is given to the prescription of driver equations for tensors, for which we give an example of how treating tensor components as scalars can lead to undesired behaviour over long timescales, including spurious growth of the BH spins. A more appropriate generalization to the tensor case is given for the comoving driver, which is shown to avoid these issues. Overall, our implementation leverages state-of-the-art methods for eccentricity reduction and wave extraction with Cauchy Characteristic Evolution to simulate systems with eccentricity $\lesssim 10^{-3}$. We obtain waveforms with phase errors $\lesssim \mathcal{O}(1) \, \mathrm{rad}$ over almost 40 GW-cycles, which naturally incorporate memory contributions.

gr-qc↗

arXiv2026

Laying the foundation of the effective-one-body waveform models SEOBNRv5: improved accuracy and efficiency for spinning non-precessing binary black holes

We present SEOBNRv5HM, a more accurate and faster inspiral-merger-ringdown gravitational waveform model for quasi-circular, spinning, nonprecessing binary black holes within the effective-one-body (EOB) formalism. Compared to its predecessor, SEOBNRv4HM, the waveform model i) incorporates recent high-order post- Newtonian results in the inspiral, with improved resummations, ii) includes the gravitational modes (l, |m|) = (3, 2), (4, 3), in addition to the (2, 2), (3, 3), (2, 1), (4, 4), (5, 5) modes already implemented in SEOBNRv4HM, iii) is calibrated to larger mass-ratios and spins using a catalog of 442 numerical-relativity (NR) simulations and 13 additional waveforms from black-hole perturbation theory, iv) incorporates information from second-order gravitational self-force (2GSF) in the nonspinning modes and radiation-reaction force. Computing the unfaithfulness against NR simulations, we find that for the dominant (2, 2) mode the maximum unfaithfulness in the total mass range $10-300 M_{\odot}$ is below $10^{-3}$ for 90% of the cases (38% for SEOBNRv4HM). When including all modes up to l = 5 we find 98% (49%) of the cases with unfaithfulness below $10^{-2} (10^{-3})$, while these numbers reduce to 88% (5%) when using SEOBNRv4HM. Furthermore, the model shows improved agreement with NR in other dynamical quantities (e.g., the angular momentum flux and binding energy), providing a powerful check of its physical robustness. We implemented the waveform model in a high-performance Python package (pySEOBNR), which leads to evaluation times faster than SEOBNRv4HM by a factor 10 to 50, depending on the configuration, and provides the flexibility to easily include spin-precession and eccentric effects, thus making it the starting point for a new generation of EOBNR waveform models (SEOBNRv5) to be employed for upcoming observing runs of the LIGO-Virgo-KAGRA detectors.

gr-qc↗

arXiv2026

Foundations of Direct Waves in Schwarzschild Ringdown

Recent studies have identified a new component in black-hole ringdown from merging binaries, termed the \emph{direct wave}. This component was argued to be tied to the dynamical source evolution near the black-hole horizon, and thus to encode horizon information. Yet a firm theoretical foundation for the direct wave has been lacking. Here we fill this gap by deriving direct waves from first principles in Schwarzschild spacetime, using the causal structure of the Green's function. We show that the direct wave does not vanish and is governed by the near-horizon source dynamics. Our results establish a theoretical basis for direct waves as a probe of near-horizon dynamics, complementary to quasinormal modes.

gr-qc↗

arXiv2026

GW250114 reveals black hole horizon signatures

The horizon of a black hole, the "surface of no return", is characterized by its rotation frequency $Ω_H$ and surface gravity $κ$. A striking signature is that any infalling object appears to orbit at $Ω_H$ due to frame dragging, while its emitted signals decay exponentially at a rate set by $κ$ as a consequence of gravitational redshift. Recent theoretical work predicts that the merger phase of gravitational waves from binary black hole coalescences carries direct imprints of the remnant horizon's properties, via a "direct wave" component that (i) oscillates near $2Ω_H$, reflecting the horizon's frame dragging and the dominant quadrupole nature of the gravitational radiation, and (ii) decays at an increasing rate characterized by $κ$, with additional screening from the black hole's potential barrier. In this paper, we report observational evidence for the direct wave in GW250114, with a 90\% credible matched-filter signal-to-noise ratio of $15.8^{+0.1}_{-0.5}$ ($17.1^{+0.1}_{-0.4}$) in the LIGO Hanford (Livingston) detector. The measured properties are in full agreement with theoretical predictions. These findings establish a new observational channel to directly measure frame-dragging effects in black hole ergospheres and explore (near-)horizon physics in dynamical, strong-gravity regimes.

gr-qc↗

arXiv2026

Prompt Response from Plunging Sources in Schwarzschild Spacetime

Gravitational waves generated by moving sources in Schwarzschild spacetime can be decomposed into three principal components: quasinormal modes, tail, and prompt response. While the first two have been extensively studied, a systematic and exact treatment of the prompt response has received comparatively little attention. In this work, building on recent progress in elucidating the structure of the Green's function of the Regge-Wheeler equation, we place the prompt response on a firm theoretical footing and investigate its morphology for sources inspiraling and plunging into a Schwarzschild black hole. We find that during the inspiral phase, the prompt response is stronger than the dynamical excitation of quasinormal modes by a factor of ~1.2, with both contributions modulated by the instantaneous orbital motion. Near the waveform peak, the prompt response rapidly decays, while the quasinormal modes transition into the ringdown regime. By combining the prompt response, quasinormal modes, and tail contributions, we achieve an accurate reconstruction of the full time-domain inspiral-merger-ringdown waveform at the 99$\%$ level, thereby providing strong support for the accuracy of this decomposition. These results offer new insight into the transition from inspiral to merger and ringdown.

gr-qc↗

arXiv2026

Decomposition of Schwarzschild Green's Function

We present a formulation of the spherically decomposed Green's function for a Schwarzschild black hole, based on a decomposition into two components, $G^+$ and $G^-$, based on their large-frequency behaviour. While similar decompositions have been considered previously, here we systematically apply it to Schwarzschild spacetime and analyze its implications for the analytic structure of the Green's function in the complex-frequency plane. We show that both $G^+$ and $G^-$ possess branch cuts along the imaginary axis, which give rise to the direct part and the late-time tail, while the poles of $G^+$ correspond to the quasinormal mode spectrum. This allows us to identify a $\textit{branch-cut direct part}$, a quasinormal-mode contribution, and a late-time tail through contours adapted to different causal spacetime regions. This is in sharp contrast to Leaver's original formulation, where the prompt response is tied to a technically difficult large-arc contribution. We validate our decomposition with independent time-domain Regge-Wheeler simulations finding excellent agreement. Our results provide a practical and physically transparent framework for disentangling the distinct pieces of the Schwarzschild response, and offer a natural starting point for extensions to Kerr perturbations and non-linear ringdown physics.

gr-qc↗

arXiv2026

Gauge Boundary conditions to mitigate center-of-mass drift in BBH simulations

Long-term numerical relativity (NR) simulations of binary black hole (BBH) systems in the Spectral Einstein Code (SpEC) code exhibit an unexpected exponential drift of the center-of-mass (CoM) away from the simulation's origin. In our work, we analyze this phenomenon and demonstrate that it is not a physical effect but rather a manifestation of a gauge artifact. The origin of this drift is the reflection of the gauge waves off the outer boundary of the computational domain. These reflections are introduced by inaccuracies in the gauge boundary condition, specifically, the application of the Sommerfeld condition to the time derivative of the gauge fields. Such an approach fails to completely suppress or correctly absorb the outgoing modes, thereby generating artificial feedback into the simulation. To mitigate this problem, we introduce a modified boundary condition that incorporates an explicit CoM correction source term designed to counteract the CoM motion. Our numerical experiments, performed with the SpEC code, reveal that this new boundary treatment reduces the CoM drift by several orders of magnitude compared to the standard implementation, and does not introduce any unwanted physical artifacts.

gr-qc↗

arXiv2026

Emergent Turbulence in Nonlinear Gravity

Gravity in nonlinear and dynamical regimes underpins spectacular astrophysical phenomena and observable consequences, from the early universe to black hole collisions. In these extreme environments, inverse energy cascades - mediated by nonlinear interactions - may help explain the near scale-invariance of cosmic structure and the simplicity of gravitational waves from binary black hole mergers. Yet the presence, characteristics, and generality of such interactions in full General Relativity remain largely unexplored. Here we show that two types of nonlinear interactions - a four-mode and a three-mode interaction - emerge in the fully nonlinear regime, and can indeed channel inverse energy cascades by inducing resonant and anti-damping instabilities. This establishes what was previously only hinted at in highly specialized perturbative contexts. We further demonstrate a ``laminar'' to ``turbulent'' transition for the largest-possible angular structure in General Relativity, whereas finer structures remain persistently turbulent. Our results reveal the impact and generality of these nonlinear interactions (instabilities), which can be key to understanding observations ranging from cosmological to kilometer scales. We anticipate that our work will shed new light on nonlinear gravitational phenomena and their consequences, such as constructing gravitational wave templates and testing General Relativity in the most extreme regime. Moreover, our work is a starting point for addressing nonlinear gravitational interactions using ideas and methods inspired by fluid dynamics.

gr-qc↗

arXiv2025

Impact of Detector Calibration Accuracy on Black Hole Spectroscopy

Systematic errors in detector calibration can bias signal analyses and potentially lead to incorrect interpretations suggesting violations of general relativity. In this study, we investigate how calibration systematics affect black hole (BH) spectroscopy, a technique that uses the quasinormal modes (QNMs) emitted during the ringdown phase of gravitational waves (GWs) to study remnant BHs formed in compact binary coalescences. We simulate a series of physically motivated, tunable calibration errors and use them to intentionally miscalibrate numerical relativity waveforms. We then apply a QNM extraction method -- the rational QNM filter -- to quantify the impact of these calibration errors. We find that current calibration standards (errors within $10\%$ in magnitude and $10^\circ$ in phase across the most sensitive frequency range of 20--2000 Hz) are adequate for BH ringdown analyses with existing observations, but insufficient for the accuracy goals of future upgraded and next-generation observatories. Specifically, we show that for events with a high ringdown signal-to-noise ratio of $\sim 120$, calibration errors must remain $\lesssim 4\%$ in magnitude and $\lesssim 4^\circ$ in phase to avoid introducing biases. While this analysis focuses on a particular aspect of BH spectroscopy, the results offer quantitative benchmarks for calibration standards crucial to fully realize the potential of precision tests of general relativity in the next-generation detector era.

gr-qc↗

arXiv2025

Probing Direct Waves in Black Hole Ringdowns

Merger gravitational waves from binary black hole coalescence carry rich information about the underlying spacetime dynamics. We analyze merger waves from comparable-mass and extreme-mass-ratio binaries, obtained from numerical relativity and black-hole perturbation theory, respectively, and argue that they are dominated by the prompt wave emissions as the black holes collide. This signal, which we refer to as the direct wave, is modulated by the plunging motion and selectively screened by the gravitational potential of the remnant black hole. The direct wave typically exhibits a time-dependent frequency and decay rate, but for high-spin remnants $(\gtrsim0.7)$ the ergosphere renders it mode-like, with a quasi-stable instantaneous oscillation frequency close to the superradiant frequency. We further estimate its detectability in a GW150914-like system and find that the signal-to-noise ratio can exceed $\sim 10$ with the current ground-based detector network. Our results therefore identify the direct wave as a robust observable for analyzing black hole ringdowns in current and future gravitational wave events.

gr-qc↗

arXiv2025

Statistical identification of ringdown modes with rational filters

Measuring quasinormal modes (QNMs) during the ringdown phase of binary black hole coalescences provides key insights into merger dynamics and enables tests of the no-hair theorem. The QNM rational filter has recently been introduced as a technique to identify specific QNMs in ringdown signals without sampling over mode amplitudes and phases. In this work, we extend the QNM rational filter framework to quantify the statistical confidence of subdominant mode detections in real gravitational wave (GW) observations. We employ a frequentist approach to estimate false-alarm probabilities and propose a workflow for robust identification of specific QNMs. We first validate our methodology using synthetic signals generated from numerical relativity waveforms. We then reanalyze the first GW event, GW150914, finding a marginal detection of an overtone, but at time when the applicability of constant amplitude QNM fits is not fully understood. This extended methodology provides a systematic approach to improving the reliability of QNM detections, paving the way for more precise tests of strong-field gravity with current and future GW observations.

gr-qc↗

arXiv2025

Signatures of Quantum Gravity in Gravitational Wave Memory

We study the impact of quantum corrections to gravitational waveforms on the gravitational wave memory effect. In certain quantum gravity theories and semi-classical frameworks, black holes (or other exotic compact objects) exhibit reflective properties that cause quasi-normal modes of a binary merger waveform to partially reflect off the horizon. If these reflections reach the detector, the measured gravitational wave signal may show echo-like features following the initial ringdown phase. Detecting such echoes, or their indirect signatures, would offer compelling evidence for the quantum nature of black holes. Given that direct detection of echoes requires finely tuned waveform templates, exploring alternative imprints of this phenomenon is crucial. In this work, we pursue this goal by calculating corrections to the null memory arising from echo-like features, formulated in terms of the Newman-Penrose scalar $Ψ_0$. We demonstrate that the morphology of the resulting features is model-independent rendering them conceptually much easier to detect in real interferometer data than the raw echo. The corresponding signal-to-noise ratio of echo-induced features appearing in the gravitational wave memory is estimated subsequently. We further compute the physical fluxes associated to the echo at both the black hole horizon and null infinity and identify novel distinguishing features of the underlying reflectivity models in measurement data.

gr-qc↗