arXiv subjects

Rico K. L. Lo

Publications and source records attributed to Rico K. L. Lo.

At least 19 recordsLinked to original sources

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

Probability of gravitational-wave lensing by intermediate-mass black holes and globular clusters

Strongly lensed gravitational waves (GWs) are powerful probes of substructure in the lens. Intermediate-mass black holes (IMBHs) are postulated to be efficient lenses that may distort the lensed waveforms of currently detectable stellar-mass compact binaries, as hinted by GW231123. Assuming that IMBHs are located in globular clusters (GCs), we compute the rate at which they would affect strongly lensed repeated chirps produced by galaxy-scale lenses, considering a compound lens system. Exploring different astrophysical model assumptions and lensing criteria, we find that the relative rate is at most 1/1000 and decays to 1/10,000 for our fiducial optimistic scenario. At high magnifications, $μ$ > 100, the relative rate approaches 1%, but these cases are intrinsically rare in absolute value. Our results imply that GW lensing by IMBHs and GCs is unlikely, disfavoring such an interpretation for GW231123. In turn, they point towards lensed GWs being a clean probe of dark matter substructures and primordial black holes.

astro-ph.CO↗

arXiv2026

Discovering gravitational waveform distortions from lensing: A deep dive into GW231123

Gravitational waves (GWs) are unique messengers as they travel through the Universe without alteration except for gravitational lensing. Their long wavelengths make them susceptible to diffraction by cosmic structures, providing an unprecedented opportunity to map dark matter substructures. Identifying lensed events requires the analysis of thousands to millions of simulated events to reach high statistical significances. This is computationally prohibitive with standard GW parameter estimation methods. We exploit DINGO-lensing, a deep-learning algorithm that accelerates the inference from CPU days to minutes to thoroughly reanalyze GW231123, the most promising lensing candidate to date. By performing more than 200,000 simulations with 3 different waveform models, we find that its statistical significance is below 4$σ$ and the event cannot be claimed as lensed. We observe that 8% of GW231123-like nonlensed simulations favor lensing, which could be explained by the self-similarity of short-duration signals. Still, 58% of GW231123-like lensed simulations have larger support for lensing, showing that higher detection statistics are possible. We show that analyzing simulations with different waveform models only lowers the significance, highlighting the relevance of waveform systematics. Although GW231123 exposes the challenges of claiming the first GW lensing detection, our deep-learning methods have demonstrated to be powerful enough to enable the upcoming discovery of lensed GWs.

gr-qc↗

arXiv2026

Gravitational radiation from Kerr black holes using the Sasaki-Nakamura formalism: Waveforms and fluxes at infinity

In linear perturbation theory for Kerr black holes, there are two equivalent formalisms, namely the Teukolsky and the Sasaki-Nakamura (SN) formalism. Typically, one defaults to the Teukolsky formalism, especially when calculating extreme mass ratio inspiral waveforms, and uses the SN formalism when dealing with extended sources, as it offers superior convergence when employing the Green's function method for calculating the inhomogeneous solution. In this work, we present a new scheme for solving the inhomogeneous SN equation, based on integration by parts, that eliminates the extra radial integration step required in the standard formulation to construct the source term for convolution with the SN variable. We derive also a SN source term that is valid for point particles on arbitrary motions around Kerr black holes. Our approach enables efficient computations of gravitational waveforms within the SN formalism in all cases, from compact to extended sources. We validate our scheme and code implementation against the literature and find excellent agreement, achieving comparable performance without employing any special optimization techniques.

gr-qc↗

arXiv2026

Near-horizon gravitational perturbations of rotating black holes

Perturbative calculations of gravitational radiation near the horizons of rotating black holes in the frequency domain have been plagued by divergence issues. We resolve this longstanding obstacle by constructing a nonsingular source term for near-horizon gravitational perturbations, or equivalently perturbed Weyl scalars $ψ_0$ with a spin weight of $s = +2$, within the generalized Sasaki-Nakamura formalism for the first time. As illustrative applications, we compute the dynamical deformation of the event horizon induced by an ultrarelativistic particle plunge, demonstrating the excitation of quasinormal modes at the horizon, and we evaluate the energy flux towards the horizon from an extreme mass-ratio inspiral. This work provides a powerful tool for studying physics near black hole horizons.

gr-qc↗

arXiv2026

Identification and characterization of distorted gravitational waves by lensing using deep learning

Gravitational waves (GWs) can be distorted by intervening mass distributions while propagating, leading to frequency-dependent modulations that imprint a distinct signature on the observed waveforms. Bayesian inference for GW lensing with conventional sampling methods is costly, and the problem is exacerbated by the rapidly growing GW catalog. Moreover, assessing the statistical significance of lensed candidates requires thousands, if not millions, of simulations to estimate the background from noise fluctuations and waveform systematics, which is infeasible with standard samplers. We present a novel method, DINGO-lensing, for performing inference on lensed GWs, extending the neural posterior estimation framework DINGO. By comparing our results with those using conventional samplers, we show that the compute time of parameter estimation of lensed GWs can be reduced from weeks to seconds, while preserving accuracy both in the posterior distributions and the evidence ratios. We train our neural networks with LIGO detector noise at design sensitivity and a lens model that accommodates two overlapping images with a constant $π/2$ phase shift. We show that the lensing parameters are recovered with millisecond precision for the time delays. We also demonstrate that our network can identify signals diffracted by point masses, highlighting its flexibility for searches. By simulating thousands of lensed and nonlensed events, we determine how the detectability changes with different source properties. DINGO-lensing provides a scalable and efficient avenue for identifying and characterizing gravitationally lensed GW events in the upcoming observing runs.

gr-qc↗

arXiv2025

Using overlap of sky localization probability maps for filtering potentially lensed pairs of gravitational-wave signals

Strong gravitational lensing creates multiple images of a gravitational wave transient. The current state-of-the-art method for identifying such lensing events is a computationally expensive full Bayesian analysis. In this paper, we investigate the feasibility and efficiency of using the overlap of sky localization probability maps (skymaps) to quickly filter potentially lensed gravitational wave signal pairs. We introduce three overlap statistics and test their performance using 200 simulated lensed pairs of gravitational-wave signals across five sets of signal-to-noise ratios. By setting a threshold with a false positive rate of $\mathrm{FPR} = 10^{-2}$ for the three overlap statistics, we find that we can filter out over $99\%$ of nonlensed events while retaining all lensed events. The statistics for each event pair can be computed instantly, and can be used in practice to quickly analyze existing events using the skymaps from the low-latency localization pipelines when results from the full parameter estimation are not available.

gr-qc↗

arXiv2025

Effects of Galaxy Cluster Structure on Lensed Gravitational Waves

Strong gravitational lenses come in many forms, but are typically divided into two populations: galaxies, and groups and clusters of galaxies. The largest objects in the Universe (i.e. galaxy clusters) are highly irregular and composed of many components due to a history of (or active) hierarchical mergers. In this work, we analyze the discrepancies in the observables of strongly lensed gravitational wave transients in both scenarios, namely relative magnifications, time delays, and image multiplicities. We compare the detection rates between the single spherical dark matter halo models found in the literature, and publicly available state-of-the-art cluster lens models. We find there to be approximately an order of magnitude fewer detection of strongly lensed transients in the realistic model case, likely caused by their loss of overall strong lensing optical depth. We also report detection rates in the weak lensing or single-image regime. Additionally, we find a systemic shift towards lower time delays between the brightest image pairs in the cases of the realistic models, as well as higher fractions of positive versus negative parity images, which was previously reported in the literature. This deviation in the joint relative magnification factor-time delay distribution will hinder the feasibility of the reconstruction of cluster-scale lenses through gravitational wave transients alone, but can still provide a lower limit on the lens mass.

astro-ph.CO↗

arXiv2025

Diffraction around caustics in gravitational wave lensing

Gravitational lensing magnification is maximal around caustics. At these source locations, an incoming wave from a point source would formally experience an infinite amplification in the high-frequency or geometric optics limit. This divergence reflects the break-down of the mathematical formalism, which is regularized by either the finite size of the source or its wavelength. We explore diffraction around caustics and their implications for the distortion of waveforms from point sources, focusing on three types of caustics: point singularities, folds, and cusps. We derive analytical results for the amplitude and phase of the diffracted waves, and compare those against the stationary phase approximation. We then study the observational signatures and detectability of these distortions on gravitational waves. We find that the lensing distortions could be detectable, but that the stationary phase approximation is still a good description of the system even close to the caustic, when the repeated gravitational wave chirps interfere with each other. We also quantify the possibility of distinguishing lensed signals from different caustics by performing Bayesian parameter estimation on simulated signals. Our results demonstrate that the universal distortions due to diffraction around caustics could be used to single out a gravitational wave event as lensed.

gr-qc↗

arXiv2025

LensingFlow: An Automated Workflow for Gravitational Wave Lensing Analyses

In this work, we present LensingFlow. This is an implementation of an automated workflow to search for evidence of gravitational lensing in a large series of gravitational wave events. This workflow conducts searches for evidence in all generally considered lensing regimes. The implementation of this workflow is built atop the Asimov automation framework and CBCFlow metadata management software and the resulting product therefore encompasses both the automated running and status checking of jobs in the workflow as well as the automated production and storage of relevant metadata from these jobs to allow for later reproduction. This workflow encompasses a number of existing lensing pipelines and has been designed to accommodate any additional future pipelines to provide both a current and future basis on which to conduct large scale lensing analyses of gravitational wave signal catalogues. The workflow also implements a prioritisation management system for jobs submitted to the schedulers in common usage in computing clusters ensuring both the completion of the workflow across the entire catalogue of events as well as the priority completion of the most significant candidates. As a first proof-of-concept demonstration, we deploy LensingFlow on a mock data challenge comprising 10 signals in which signatures of each lensing regime are represented. LensingFlow successfully ran and identified the candidates from this data through its automated checks of results from consituent analyses.

gr-qc↗

arXiv2025

Phase consistency test to identify type II strongly lensed gravitational wave signals using a single event

For gravitationally lensed type II signals, the phase of the dominant (2, 2) mode and the higher order (3, 3) mode is offset by $-π/12$, or roughly -0.26 radians. Using this, we develop a test for type II imagery by allowing the phases of the (2,2) and (3,3) modes to vary separately and introducing a new waveform parameter to represent the phase offset between the two. We use simulated, asymmetric mass ratio, precessing signals to show that the test can reproduce the $-π/12$ phase offset when detected by three detectors for H-L optimal SNR $\gtrsim$ 40 and $\mathcal{M} \leq 30$. We analyze GW190412 and GW190814 using this parameterization, measuring the offset to be $0.13^{+0.22}_{-0.17}$ for GW190412 and $-0.05^{+0.20}_{-0.22}$ for GW190814. We also measure the Bayes factor in support of zero phase offset, $\log_{10} \mathcal{B}_{Δφ= 0}$, to be $-0.14$ for GW190412 and $0.21$ for GW190814. This implies our results are not strong enough to confidently argue if either event is a type II image, and is consistent with our statistical analysis.

gr-qc↗

arXiv2025

Quasinormal modes and excitation factors of Kerr black holes

Theoretical understanding of the characteristic oscillations of a perturbed black hole, also referred to as quasinormal modes (QNMs), is crucial to interpreting the late stage of binary black hole mergers that we now routinely observe in gravitational wave detectors. In this work, we introduce a new approach, based on the generalized Sasaki-Nakamura formalism, to compute the QNM spectra and their excitation factors (QNEFs), for scalar, electromagnetic and gravitational perturbations. Using this approach, QNM wavefunctions remain finite at the horizon and spatial infinity. Our results in general agree with previous calculations that were performed using different methods, though we further clarify that QNEFs and their scaling with the mass of the black hole depend on the spin-weight of the perturbation. We show that avoided crossing is not a general phenomenon: the real or the imaginary part of the eigenvalues can cross each other but not both simultaneously, and when crossing occurs in one part, repulsion follows in the another part. Eigenvalue repulsion, originating from branch point singularities, still plays an important role in the QNM spectra, despite the fact that the spectra depend only on the real-valued black hole angular momentum.

gr-qc↗

arXiv2025

Observational Signatures of Highly Magnified Gravitational Waves from Compact Binary Coalescence

Gravitational lensing has empowered telescopes to discover astronomical objects that are otherwise out of reach without being highly magnified by foreground structures. While we expect gravitational waves (GWs) from compact binary coalescences to also experience lensing, the phenomenology of highly magnified GWs has not been fully exploited. In this Letter, we fill this gap and explore the observational signatures of these highly magnified GWs. We find that these signatures are robust against modeling details and can be used as smoking-gun evidence to confirm the detection of lensing of GWs without any electromagnetic observation. Additionally, diffraction becomes important in some cases, which limits the maximum possible magnification and gives waveform signatures of lensing that can only be observed by GW detectors. Even with current-generation observatories, we are already sensitive to these rare, highly magnified GWs and could use them to probe the high-redshift Universe beyond the usual horizon.

gr-qc↗

arXiv2025

Multi-messenger Gravitational Lensing

We introduce the rapidly emerging field of multi-messenger gravitational lensing - the discovery and science of gravitationally lensed phenomena in the distant universe through the combination of multiple messengers. This is framed by gravitational lensing phenomenology that has grown since the first discoveries in the 20th century, messengers that span 30 orders of magnitude in energy from high energy neutrinos to gravitational waves, and powerful "survey facilities" that are capable of continually scanning the sky for transient and variable sources. Within this context, the main focus is on discoveries and science that are feasible in the next 5-10 years with current and imminent technology including the LIGO-Virgo-KAGRA network of gravitational wave detectors, the Vera C. Rubin Observatory, and contemporaneous gamma/X-ray satellites and radio surveys. The scientific impact of even one multi-messenger gravitational lensing discovery will be transformational and reach across fundamental physics, cosmology and astrophysics. We describe these scientific opportunities and the key challenges along the path to achieving them. This article is the introduction to the Theme Issue of the Philosophical Transactions of The Royal Society A on the topic of Multi-messenger Gravitational Lensing, and describes the consensus that emerged at the associated Theo Murphy Discussion Meeting in March 2024.

astro-ph.HE↗

arXiv2025

Constraining Proper Motion of Strongly Lensed Eccentric Binary Mergers using Doppler Triangulation

Strong lensing of gravitational wave (GW) sources allows the observer to see the GW source from different lines-of-sight (LOS) through the corresponding images, which provides a way for constraining the relative proper motion of the GW source. This is possible as the GW signals received from each image will have slightly different projected velocity components, from which one can `Doppler-Triangulate' for the GW source velocity vector. The difference in projected velocity between the different images can be observationally inferred through pairwise GW phase measurements that accumulate over the time-of-observation. In this paper we study lensed eccentric GW sources and explore how the observable GW phase shift between images evolve as a function of time, eccentricity, lens- and binary parameters. Next generation GW observatories, including the Einstein Telescope and Cosmic Explorer, will see $\sim $hundreds/year of lensed GW sources, where a significant fraction of these are expected to be eccentric. We discuss the expected unique observables for such eccentric lensed GW sources, and the relation to their observable relative linear motion, which otherwise is exceedingly difficult to constrain in general.

astro-ph.HE↗

arXiv2025

Recipes for computing radiation from a Kerr black hole using a generalized Sasaki-Nakamura formalism: Homogeneous solutions

Central to black hole perturbation theory calculations is the Teukolsky equation that governs the propagation and the generation of radiation emitted by Kerr black holes. However, it is plagued by a long-ranged potential associated with the perturbation equation and hence a direct numerical integration of the equation is challenging. Sasaki and Nakamura devised a formulation that transforms the equation into a new equation that is free from the issue for the case of outgoing gravitational radiation. The formulation was later generalized by Hughes to work for any type of radiation. In this work, we revamp the Generalized Sasaki-Nakamura (GSN) formalism and explicitly show the transformations that convert solutions between the Teukolsky and the GSN formalism for both in- and outgoing radiation of scalar, electromagnetic, and gravitational type. We derive all necessary ingredients for the GSN formalism to be used in numerical computations. In particular, we present a new numerical implementation of the formalism, GeneralizedSasakiNakamura.jl, that computes homogeneous solutions to both perturbation equations in the Teukolsky and the GSN formalism. The code works well at low frequencies and is even better at high frequencies by leveraging the fact that black holes are highly permeable to waves at high frequencies. This work lays the foundation for an efficient scheme to compute gravitational radiation from Kerr black holes and an alternative way to compute quasinormal modes of Kerr black holes.

gr-qc↗

arXiv2024

Measuring the Transverse Velocity of Strongly Lensed Gravitational Wave Sources with Ground Based Detectors

Observations of strongly gravitationally lensed gravitational wave (GW) sources provide a unique opportunity for constraining their transverse motion, which otherwise is exceedingly hard for GW mergers in general. Strong lensing makes this possible when two or more images of the lensed GW source are observed, as each image essentially allows the observer to see the GW source from different directional lines-of-sight. If the GW source is moving relative to the lens and observer, the observed GW signal from one image will therefore generally appear blue- or redshifted compared to GW signal from the other image. This velocity induced differential Doppler shift gives rise to an observable GW phase shift between the GW signals from the different images, which provides a rare glimpse into the relative motion of GW sources and their host environment across redshift. We illustrate that detecting such GW phase shifts is within reach of next-generation ground-based detectors such as Einstein Telescope, that is expected to detect $\sim$hundreds of lensed GW mergers per year. This opens up completely new ways of inferring the environment of GW sources, as well as studying cosmological velocity flows across redshift.

astro-ph.HE↗

arXiv2024

What is the nature of GW230529? An exploration of the gravitational lensing hypothesis

On the 29th of May 2023, the LIGO-Virgo-KAGRA Collaboration observed a compact binary coalescence event consistent with a neutron star-black hole merger, though the heavier object of mass 2.5-4.5 $M_\odot$ would fall into the purported lower mass gap. An alternative explanation for apparent observations of events in this mass range has been suggested as strongly gravitationally lensed binary neutron stars. In this scenario, magnification would lead to the source appearing closer and heavier than it really is. Here, we investigate the chances and possible consequences for the GW230529 event to be gravitationally lensed. We find this would require high magnifications and we obtain low rates for observing such an event, with a relative fraction of lensed versus unlensed observed events of $2 \times 10^{-3}$ at most. When comparing the lensed and unlensed hypotheses accounting for the latest rates and population model, we find a 1/58 chance of lensing, disfavoring this option. Moreover, when the magnification is assumed to be strong enough to bring the mass of the heavier binary component below the standard limits on neutron star masses, we find high probability for the lighter object to have a sub-solar mass, making the binary even more exotic than a mass-gap neutron star-black hole system. Even when the secondary is not sub-solar, its tidal deformability would likely be measurable, which is not the case for GW230529. Finally, we do not find evidence for extra lensing signatures such as the arrival of additional lensed images, type-II image dephasing, or microlensing. Therefore, we conclude it is unlikely for GW230529 to be a strongly gravitationally lensed binary neutron star signal.

gr-qc↗