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The gravitational physics landscape is evolving rapidly, driven by our ability to study strong-field regions, in particular black holes. Black Holes Inside and Out gathered world experts to discuss the status of the field and prospects ahead. We hope that the ideas and perspectives are a source of inspiration. Structure: Black Hole Evaporation - 50 Years by William Unruh The Stability Problem for Extremal Black Holes by Mihalis Dafermos The Entropy of Black Holes by Robert M. Wald The Non-linear Regime of Gravity by Luis Lehner Black Holes Galore in D > 4 by Roberto Emparan Same as Ever: Looking for (In)variants in the Black Holes Landscape by Carlos A. R. Herdeiro Black Holes, Cauchy Horizons, and Mass Inflation by Matt Visser The Backreaction Problem for Black Holes in Semiclassical Gravity by Adrian del Rio Black Holes Beyond General Relativity by Enrico Barausse and Jutta Kunz Black Holes as Laboratories: Searching for Ultralight Fields by Richard Brito Primordial Black Holes from Inflation by Misao Sasaki Tests of General Relativity with Future Detectors by Emanuele Berti Black Holes as Laboratories: Tests of General Relativity by Ruth Gregory and Samaya Nissanke Simulating Black Hole Imposters by Frans Pretorius Black Hole Spectroscopy: Status Report by Gregorio Carullo VLBI as a Precision Strong Gravity Instrument by Paul Tiede Testing the nature of compact objects and the black hole paradigm by Mariafelicia De Laurentis and Paolo Pani Some Thoughts about Black Holes in Asymptotic Safety by Alessia Platania Black Hole Evaporation in Loop Quantum Gravity by Abhay Ashtekar How the Black Hole Puzzles are Resolved in String Theory by Samir D. Mathur Quantum Black Holes: From Regularization to Information Paradoxes by Niayesh Afshordi and Stefano Liberati, Comment: 221 pages, 21 contributions

We study the robustness of parametrized tests of General Relativity (GR) with gravitational waves due to waveform inaccuracy. In particular, we determine the properties of the signal (signal-to-noise ratio (SNR) and source parameters) such that we are led to falsely identify a GR deviation due to neglecting spin precession or higher models in the recovery model. To characterize the statistical significance of the biases, we compute the Bayes factor between the non-GR and GR models, and the fitting factor of the non-GR model. For highly-precessing, edge-on signals, we find that mismodeling the signal leads to a significant systematic bias in the recovery of the non-GR parameter, even at an SNR of 30. However, these biased inferences are characterized by a significant loss of SNR and a weak preference for the non-GR model (over the GR model). At a higher SNR, the biased inferences display a strong preference for the non-GR model (over the GR model) and a significant loss of SNR. For edge-on signals containing asymmetric masses, at an SNR of 30, we find that excluding higher modes does not impact the ppE tests as much as excluding spin precession. Our analysis, therefore, identifies the spin-precessing and mass-asymmetric systems for which parametrized tests of GR are robust. With a toy model and using the linear signal approximation, we illustrate these regimes of bias and characterize them by obtaining bounds on the ratio of systematic to statistical error and the effective cycles incurred due to mismodeling. As a by-product of our analysis, we explicitly connect different measures and techniques commonly used to estimate systematic errors -- linear-signal approximation, Laplace approximation, fitting factor, effective cycles, and Bayes factor -- that are generally applicable to all studies of systematic uncertainties in gravitational wave parameter estimation., Comment: 51 pages, 22 figures, 5 tables

The spin of intermediate-mass black holes (IMBHs) growing through repeated black hole mergers in stellar clusters statistically asymptotes to zero. Putative observations of IMBHs with dimensionless spin parameter $\chi\gtrsim 0.6$ would require a phase of coherent gas accretion to spin up the black hole. We estimate the amount of gas necessary to produce a given IMBH spin. If the observed IMBH mass and spin are $M\gtrsim 1000~M_\odot$ and $\chi\gtrsim 0.6$, respectively, the IMBH must have coherently accreted at least $\sim 100~M_\odot$ of gas. In this scenario, as long as the spin is not maximal, the IMBH can only accrete at most half of its mass. Our estimates can constrain the relative contribution of accretion and mergers to the growth of IMBHs in dense stellar environments., Comment: 10 pages, 7 figures

Recent work has shown that the quasinormal mode spectrum of black holes is unstable under small perturbations (of order $\epsilon$) of the radial potential, while the early time-domain ringdown waveform is only marginally affected. In this paper we provide further insight into the apparent tension between the frequency-domain and the time-domain descriptions by analyzing the scattering properties of the problem. In the frequency domain, we study analytically the solutions corresponding to the perturbed potential. We show that there are two qualitatively different classes of instabilities, and that both Schwarzschild and Kerr black holes are affected by what we call a "Type II" instability, i.e., an exponential migration of the mode frequencies away from their unperturbed value as the perturbing "bump" moves away from the peak of the unperturbed potential. In the time domain, we elucidate the effect of the spectral instability in terms of the causal structure of the Green's function. By using an equivalent scattering problem we confirm analytically (and show numerically) that the deviation from the unperturbed waveform in the early ringdown stage is proportional to $\epsilon$ when $\epsilon\lesssim10^{-2}$., Comment: 18 pages, 8 figures

Stochastic gravitational-wave backgrounds can be of either cosmological or astrophysical origin. The detection of an astrophysical stochastic gravitational-wave background with ground-based interferometers is expected in the near future. Perhaps even more excitingly, the detection of stochastic backgrounds of cosmological origin by future ground-based interferometers could reveal invaluable information about the early Universe. From this perspective, the astrophysical background is a {\it foreground} that can prevent the extraction of this information from the data. In this paper, we revisit a time-frequency domain notching procedure previously proposed to remove the astrophysical foreground in the context of next-generation ground-based detectors, but we consider the more realistic scenario where we remove individually detectable signals by taking into account the uncertainty in the estimation of their parameters. We find that time-frequency domain masks can still efficiently remove the astrophysical foreground and suppress it to about $5\%$ of its original level. Further removal of the foreground formed by unresolvable events (in particular, unresolvable binary neutron stars), which is about $10$ times larger than the residual foreground from realistic notching, would require detector sensitivity improvements. Therefore, the main limitation in the search for a cosmological background is the unresolvable foreground itself, and not the residual of the notching procedure., Comment: 13 pages, 6 figures

Astrophysical scenarios for the formation and evolution of intermediate-mass black holes (IMBHs) in the mass range $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$ remain uncertain, but future ground-based gravitational-wave (GW) interferometers will probe the lower end of the IMBH mass range. We study the detectability of IMBH binary mergers and the measurability of their parameters with next-generation ground-based detector networks consisting of various combinations of Cosmic Explorer (CE) and Einstein Telescope (ET) interferometers. We find that, for binaries with component masses $m_{1,2}\sim 1000\,M_\odot$, an optimal 3-detector network can constrain the masses with errors $\lesssim 0.1\%$ ($\lesssim 1\%$) at $z=0.5$ ($z=2$), and the source redshift can be measured with percent-level accuracy or better at $z\lesssim 2$. The redshift of lighter binaries ($m_{1,2}\lesssim 300\,M_\odot$) can still be measured with $O(10)\%$ accuracy even at $z=10$. Binaries with $z\lesssim 0.5$ can be localized within $1\,\rm{deg}^2$ for $m_{1,2}\lesssim 1000\,M_\odot$, and within $0.1\,\rm{deg}^2$ for comparable mass systems. The sky localization is good enough that it may be possible to cross-correlate GW searches with galaxy catalogs and to search for electromagnetic counterparts to IMBH mergers. We also point out that the low-frequency sensitivity of the detectors is crucial for IMBH detection and parameter estimation. It will be interesting to use our results in conjunction with population synthesis codes to constrain astrophysical IMBH formation models., Comment: 16 pages, 8 figures. All data are available at https://doi.org/10.5281/zenodo.11450792

Galactic double white dwarf (DWD) binaries are among the guaranteed sources for the Laser Interferometer Space Antenna (LISA), an upcoming space-based gravitational wave (GW) detector. Most DWDs in the LISA band are far from merging and emit quasimonochromatic GWs. As these sources are distributed throughout the Milky Way, they experience different accelerations in the Galactic gravitational potential, and therefore each DWD exhibits an apparent GW frequency chirp due to differential acceleration between the source and LISA. We examine how Galactic acceleration influences parameter estimation for these sources; and investigate how LISA observations could provide insight into the distribution of matter in the Galaxy., Comment: 20 pages, 7 figures

General relativity (GR) has proven to be a highly successful theory of gravity since its inception. The theory has thrivingly passed numerous experimental tests, predominantly in weak gravity, low relative speeds, and linear regimes, but also in the strong-field and very low-speed regimes with binary pulsars. Observable gravitational waves (GWs) originate from regions of spacetime where gravity is extremely strong, making them a unique tool for testing GR, in previously inaccessible regions of large curvature, relativistic speeds, and strong gravity. Since their first detection, GWs have been extensively used to test GR, but no deviations have been found so far. Given GR's tremendous success in explaining current astronomical observations and laboratory experiments, accepting any deviation from it requires a very high level of statistical confidence and consistency of the deviation across GW sources. In this paper, we compile a comprehensive list of potential causes that can lead to a false identification of a GR violation in standard tests of GR on data from current and future ground-based GW detectors. These causes include detector noise, signal overlaps, gaps in the data, detector calibration, source model inaccuracy, missing physics in the source and in the underlying environment model, source misidentification, and mismodeling of the astrophysical population. We also provide a rough estimate of when each of these causes will become important for tests of GR for different detector sensitivities. We argue that each of these causes should be thoroughly investigated, quantified, and ruled out before claiming a GR violation in GW observations., Comment: Review article; 1 figure; 1 table; comments welcome

In this work we compute numerical bounds on the mass $\mu$ of superradiantly unstable scalar fields in a Kerr black hole background using the continued fraction method. We show that the normalized upper bound on the mass $\mu$ increases with the angular momentum number $\ell$ and the azimuthal number $m$, approaching the most stringent analytical bound known to date when $\ell=m \gg 1$. We also provide an analytical fit to the numerically determined mass bound as a function of the dimensionless spin parameter $a/M$ of the black hole with an accuracy of the order $0.1\%$ for the fundamental mode with $\ell=m=1$, and of the order $1\%$ for higher-order modes (up to $\ell=m=20$). We argue that this analytical fit is particularly useful in astrophysical scenarios, since the lowest $\ell=m$ modes are capable of producing the strongest observable imprints of superradiance., Comment: 8 pages, 7 figures. v2: typos corrected, reference added

Rapid formation of supermassive black holes occurs in dense nuclear star clusters that are initially gas-dominated. Stellar-mass black hole remnants of the most massive cluster sink into the core, where a massive runaway black hole forms as a consequence of combined effects of repeated mergers and Eddington-limited gas accretion. The associated gravitational wave signals of high-redshift extreme mass-ratio inspirals are a unique signature of the nuclear star cluster scenario., Comment: 4 pages, 3 figures

Fermion soliton stars are a consistent model of exotic compact objects which involve a nonlinear interaction between a real scalar field and fermions through a Yukawa term. This interaction results in an effective fermion mass that depends upon the vacuum structure in the scalar potential. In this work we investigate the tidal deformations of fermion soliton stars and compute the corresponding tidal Love numbers for different model parameters. Furthermore, we discuss the existence of approximate universal relations for the electric and magnetic tidal deformabilities of these stars, and compare them with other solutions of general relativity, such as neutron stars or boson stars. These relations for fermion soliton stars are less universal than for neutron stars, but they are sufficiently different from the ordinary neutron star case that a measurement of the electric and magnetic tidal Love numbers (as potentially achievable by next-generation gravitational wave detectors) can be used to disentangle these families of compact objects. Finally, we discuss the conditions for tidal disruption of fermion soliton stars in a binary system and estimate the detectability of the electromagnetic signal associated with such tidal disruption events., Comment: 15 pages, 4 figures. v2: new figure added, matches version accepted in PRD

Next-generation gravitational wave detectors such as the Einstein Telescope and Cosmic Explorer will have increased sensitivity and observing volumes, enabling unprecedented precision in parameter estimation. However, this enhanced precision could also reveal systematic biases arising from waveform modeling, which may impact astrophysical inference. We investigate the extent of these biases over a year-long observing run with $10^5$ simulated binary black hole sources using the linear signal approximation. To establish a conservative estimate, we sample binaries from a smoothed truncated power-law population model and compute systematic parameter biases between the IMRPhenomXAS and IMRPhenomD waveform models. For sources with signal-to-noise ratios above 100, we estimate statistically significant parameter biases in $\sim 3\%-20\%$ of the events, depending on the parameter. We find that the average mismatch between waveform models required to achieve a bias of $\leq 1\sigma$ for $99\%$ of detections with signal-to-noise ratios $\geq 100$ should be $\mathcal{O}(10^{-5})$, or at least one order of magnitude better than current levels of waveform accuracy., Comment: 15 pages, 11 figures, 1 table. Matches the version published in Phys. Rev. D 109, 104043

When gravitational waves pass near a gravitating object, they are deflected, or lensed. If the object is massive, such that the wavelength of the waves is small compared to its gravitational size, lensed gravitational wave events can be identified when multiple signals are detected at different times. However, when the wavelength is long, wave-optics diffraction effects will be important, and a lensed event can be identified by looking for frequency-dependent modulations to the gravitational waveform, without having to associate multiple signals. For current ground-based gravitational wave detectors observing stellar-mass binary compact object mergers, wave-optics effects are important for lenses with masses $\lesssim 1000 M_{\odot}$. Therefore, minihalos below this mass range could potentially be identified by lensing diffraction. The challenge with analyzing these events is that the frequency-dependent lensing modulation, or the amplification factor, is prohibitively expensive to compute for Bayesian parameter inference. In this work, we use a novel time-domain method to construct interpolators of the amplification factor for the Navarro-Frenk-White (NFW), generalized singular isothermal sphere (gSIS) and cored isothermal sphere (CIS) lens models. Using these interpolators, we perform Bayesian inference on gravitational-wave signals lensed by minihalos injected in mock detector noise, assuming current sensitivity of ground-based detectors. We find that we could potentially identify an event when it is lensed by minihalos and extract the values of all lens parameters in addition to the parameters of the GW source. All of the methods are implemented in Glworia, the accompanying open-source Python package, and can be generalized to study lensed signals detected by current and next-generation detectors., Comment: 19 pages, 9 figures

In the aftermath of a binary black hole merger event, the gravitational wave signal emitted by the remnant black hole is modeled as a superposition of damped sinusoids known as quasinormal modes. While the dominant quasinormal modes originating from linear black hole perturbation theory have been studied extensively in this post-merger "ringdown" phase, more accurate models of ringdown radiation include the nonlinear modes arising from higher-order perturbations of the remnant black hole spacetime. We explore the detectability of quadratic quasinormal modes with both ground- and space-based next-generation detectors. We quantify how predictions of the quadratic mode detectability depend on the quasinormal mode starting times. We then calculate the signal-to-noise ratio of quadratic modes for several detectors and binary black hole populations, focusing on the ($220\times220$) mode - i.e., on the quadratic term sourced by the square of the linear $(220)$ mode. For the events with the loudest quadratic mode signal-to-noise ratios, we additionally compute statistical errors on the mode parameters in order to further ascertain the distinguishability of the quadratic mode from the linear quasinormal modes. The astrophysical models used in this paper suggest that while the quadratic mode may be detectable in at most a few events with ground-based detectors, the prospects for detection with the Laser Interferometer Space Antenna (LISA) are more optimistic., Comment: 21 pages, 16 figures, 2 tables; revised to match published version; new plots in App. D

The ground-based gravitational wave (GW) detectors LIGO and Virgo have enabled the birth of multi-messenger GW astronomy via the detection of GWs from merging stellar-mass black holes (BHs) and neutron stars (NSs). GW170817, the first binary NS merger detected in GWs and all bands of the electromagnetic spectrum, is an outstanding example of the impact that GW discoveries can have on multi-messenger astronomy. Yet, GW170817 is only one of the many and varied multi-messenger sources that can be unveiled using ground-based GW detectors. In this contribution, we summarize key open questions in the astrophysics of stellar-mass BHs and NSs that can be answered using current and future-generation ground-based GW detectors, and highlight the potential for new multi-messenger discoveries ahead., Comment: Review submitted to the Frontiers Research Topic "The Dynamic Universe: Realizing the Potential of Time Domain and Multimessenger Astrophysics"

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

In fluid dynamics, the Magnus effect is the force perpendicular to the motion of a spinning object as it moves through a medium. In general relativity, an analogous effect exists for a spinning compact object moving through matter, purely as a result of gravitational interactions. In this work we consider a Kerr black hole moving at relativistic velocities through scalar dark matter that is at rest. We simulate the system numerically and extract the total spin-curvature force on the black hole perpendicular to its motion. We confirm that the force scales linearly with the dimensionless spin parameter $a/M$ of the black hole up to $a/M = 0.99$, and measure its dependence on the speed $v$ of the black hole in the range $0.1 \le v \le 0.55$ for a fixed spin. Compared to previous analytic work applicable at small $v$, higher-order corrections in the velocity are found to be important: the total force is nonzero, and the dependence is not linear in $v$. We find that in all cases the total force is in the opposite direction to the hydrodynamical analogue, although at low speeds it appears to approach the expectation that the Weyl and Magnus components cancel. Spin-curvature effects may leave an imprint on gravitational wave signals from extreme mass-ratio inspirals, where the secondary black hole has a nonnegligible spin and moves in the presence of a dark matter cloud. We hope that our simulations can be used to support and extend the limits of analytic results, which are necessary to better quantify such effects in the relativistic regime., Comment: 10 pages, 6 figures

Stellar evolution predicts the existence of a mass gap for black hole remnants produced by pair-instability supernova dynamics, whose lower and upper edges are very uncertain. We study the possibility of constraining the location of the upper end of the pair-instability mass gap, which is believed to appear around ${m_\text{min}} \sim130M_\odot$, using gravitational wave observations of compact binary mergers with next-generation ground-based detectors. While high metallicity may not allow for the formation of first-generation black holes on the "far side" beyond the gap, metal-poor environments containing Population III stars could lead to such heavy black hole mergers. We show that, even in the presence of contamination from other merger channels, next-generation detectors will measure the location of the upper end of the mass gap with a relative precision close to $\Delta {m_\text{min}}/{m_\text{min}} \simeq 4\% (N_\text{det}/100 )^{-1/2}$ at 90% C.L., where $N_\text{det} $ is the number of detected mergers with both members beyond the gap. These future observations could reduce current uncertainties in nuclear and astrophysical processes controlling the location of the gap., Comment: 12 pages, 6 figures

We develop a numerical approach to compute polar parity perturbations within fully relativistic models of black hole systems embedded in generic, spherically symmetric, anisotropic fluids. We apply this framework to study gravitational wave generation and propagation from extreme mass-ratio inspirals in the presence of several astrophysically relevant dark matter models, namely the Hernquist, Navarro-Frenk-White, and Einasto profiles. We also study dark matter spike profiles obtained from a fully relativistic calculation of the adiabatic growth of a BH within the Hernquist profile, and provide a closed-form analytic fit of these profiles. Our analysis completes prior numerical work in the axial sector, yielding a fully numerical pipeline to study black hole environmental effects. We study the dependence of the fluxes on the DM halo mass and compactness. We find that, unlike the axial case, polar fluxes are not adequately described by simple gravitational-redshift effects, thus offering an exciting avenue for the study of black hole environments with gravitational waves., Comment: 11 pages, 5 figures, 1 table

Among the binary sources of interest for LISA some are quasimonochromatic, in the sense that the change in the gravitational wave frequency $\Delta f\lesssim 1\;\mbox{yr}^{-1}$ during the observation time. For these sources, we revisit the stationary phase approximation (SPA) commonly used in Fisher matrix calculations in the frequency domain and show how it is modified by the Doppler shift induced by LISA's motion and by the LISA pattern functions. We compare our results with previous work in the time domain and discuss the transition from the quasimonochromatic case to the conventional SPA which applies when $\Delta f\gtrsim 1\;\mbox{yr}^{-1}$., Comment: 14 pages, 9 figures; added references

Black hole spectroscopy is a clean and powerful tool to test gravity in the strong-field regime and to probe the nature of compact objects. Next-generation ground-based detectors, such as the Einstein Telescope and Cosmic Explorer, will observe thousands of binary black hole mergers with large signal-to-noise ratios, allowing for accurate measurements of the remnant black hole quasinormal mode frequencies and damping times. In previous work we developed an observable-based parametrization of the quasinormal mode spectrum of spinning black holes beyond general relativity (ParSpec). In this paper we use this parametrization to ask: can next-generation detectors detect or constrain deviations from the Kerr spectrum by stacking multiple observations of binary mergers from astrophysically motivated populations? We focus on two families of tests: (i) agnostic (null) tests, and (ii) theory-based tests, which make use of quasinormal frequency calculations in specific modified theories of gravity. We consider in particular two quadratic gravity theories (Einstein-scalar-Gauss-Bonnet and dynamical Chern-Simons gravity) and various effective field theory-based extensions of general relativity. We find that robust inference of hypothetical corrections to general relativity requires pushing the slow-rotation expansion to high orders. Even when high-order expansions are available, ringdown observations alone may not be sufficient to measure deviations from the Kerr spectrum for theories with dimensionful coupling constants. This is because the constraints are dominated by "light" black hole remnants, and only few of them have sufficiently high signal-to-noise ratio in the ringdown. Black hole spectroscopy with next-generation detectors may be able to set tight constraints on theories with dimensionless coupling, as long as we assume prior knowledge of the mass and spin of the remnant black hole., Comment: references updated

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

In this Reply we include the corrections suggested in the Comment [Phys. Rev. Lett. 131, 169001]. We show that their impact on our results is small, and that the overall conclusion of the Article [Phys. Rev. Lett. 129, 111102] are robust. As pointed out in the Article, it is crucial to account for the statistical uncertainty in the ringdown starting time, neglected in most previous studies. This uncertainty is ~40 times larger than the systematic shift induced by the software bug mentioned in the Comment. The remaining discrepancies between the Comment and the Article can be attributed to additional differences in the setup, notably the sampling rate and the noise estimation method (in the Article the latter was chosen to mimic the original methods of [Phys. Rev. Lett. 123, 111102]). Beyond data analysis considerations, the physics of the problem cannot be ignored. As shown in [arXiv:2302.03050], a model consisting of a sum of constant-amplitude overtones starting at the peak of the waveform introduces uncontrolled systematic uncertainties in the measurement due to dynamical and strong-field effects. These theoretical considerations imply that studies based on such models cannot be interpreted as black hole spectroscopy tests., Comment: 3 pages, 1 figure. Unabridged version of the shorter (due to format constraints) Reply published in Phys. Rev. Lett

In general relativity, when two black holes merge they produce a rotating (Kerr) black hole remnant. According to perturbation theory, the remnant emits "ringdown" radiation: a superposition of exponentials with characteristic complex frequencies that depend only on the remnant's mass and spin. While the goal of the black hole spectroscopy program is to measure the quasinormal mode frequencies, a knowledge of their amplitudes and phases is equally important to determine which modes are detectable, and possibly to perform additional consistency checks. Unlike the complex frequencies, the amplitudes and phases depend on the properties of the binary progenitors, such as the binary mass ratio and component spins. In this paper we develop a fitting algorithm designed to reliably identify the modes present in numerical simulations and to extract their amplitudes and phases. We apply the algorithm to over 500 binary black hole simulations from the public SXS numerical relativity simulation catalog, and we present fitting formulas for the resulting mode amplitudes and phases as functions of the properties of the progenitors. Crucially, our algorithm allows for the extraction of not only prograde fundamental modes and overtones, but also retrograde modes and second-order modes. We unveil interesting relations for the amplitude ratios of different modes. The fitting code and interactive versions of some of the plots are publicly available. The results presented in this paper can be updated as more and better simulations become available., Comment: 38 pages, 22 figures, 2 tables. Interactive plots and code usage examples available at https://mhycheung.github.io/jaxqualin/. The fitting formulas in Eq. (13) have been updated to match an erratum accepted by PRD. None of the figures are affected

The nonlinear character of general relativity leaves its imprint in the coalescence of two black holes, from the inspiral to the final ringdown stage. To quantify the impact of nonlinearities, we work at second order in black hole perturbation theory and we study the excitation of second-order modes relative to the first-order modes that drive them as we vary the black hole spin and the initial data for the perturbations. The relative amplitude of second-order modes is only mildly dependent on the initial data that we consider, but it strongly decreases for large black hole spins. This implies that the extrapolation of calculations based on the Kerr-CFT correspondence to subextremal Kerr black holes should be viewed with caution., Comment: v3 (matches published version)

Current gravitational-wave data from stellar-mass black-hole binary mergers suggest a correlation between the binary mass ratio $q$ and the effective spin $\chi_\mathrm{eff}$: more unequal-mass binaries consistently show larger and positive values of the effective spin. Multiple generations of black-hole mergers in dense astrophysical environments may provide a way to form unequal-mass systems, but they cannot explain the observed correlation on their own. We show that the symmetry of the astrophysical environment is a crucial feature to shed light on this otherwise puzzling piece of observational evidence. We present a toy model that reproduces, at least qualitatively, the observed correlation. The model relies on axisymmetric, disk-like environments where binaries participating in hierarchical mergers share a preferential direction. Migration traps in AGN disks are a prime candidate for this setup, hinting at the exciting possibility of constraining their occurrence with gravitational-wave data., Comment: 9 pages, 4 figures. Published in PRD

Gravitational-wave observations by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo have provided us a new tool to explore the Universe on all scales from nuclear physics to the cosmos and have the massive potential to further impact fundamental physics, astrophysics, and cosmology for decades to come. In this paper we have studied the science capabilities of a network of LIGO detectors when they reach their best possible sensitivity, called A#, given the infrastructure in which they exist and a new generation of observatories that are factor of 10 to 100 times more sensitive (depending on the frequency), in particular a pair of L-shaped Cosmic Explorer observatories (one 40 km and one 20 km arm length) in the US and the triangular Einstein Telescope with 10 km arms in Europe. The presence of one or two A# observatories in a network containing two or one next generation observatories, respectively, will provide good localization capabilities for facilitating multimessenger astronomy and precision measurement of the Hubble parameter. Two Cosmic Explorer observatories are indispensable for achieving precise localization of binary neutron star events, facilitating detection of electromagnetic counterparts and transforming multimessenger astronomy. Their combined operation is even more important in the detection and localization of high-redshift sources, such as binary neutron stars, beyond the star-formation peak, and primordial black hole mergers, which may occur roughly 100 million years after the Big Bang. The addition of the Einstein Telescope to a network of two Cosmic Explorer observatories is critical for accomplishing all the identified science metrics. For most metrics the triple network of next generation terrestrial observatories are a factor 100 better than what can be accomplished by a network of three A# observatories., Comment: 48 pages, 20 figures, 14 tables

The Laser Interferometer Space Antenna (LISA) will detect gravitational waves (GWs) emitted by massive black hole binaries (MBHBs) in the low-frequency ($\sim$mHz) band. Low-mass lenses, such as low-mass dark matter halos or subhalos, have sizes comparable to the wavelength of these GWs. Encounters with these lenses produce wave-optics (WO) effects that alter waveform phase and amplitude. Thus, a single event with observable WO effects can be used to probe the lens properties. In this paper, we first compute the probability of observing WO effects in a model-agnostic way. We perform information-matrix analyses over approximately 1000 MBHBs with total mass, mass ratio, and redshift spanning the ranges relevant to LISA. We then calculate lensing rates using three semi-analytical models of MBHB populations. In both cases, we use a waveform model that includes merger, ringdown, and higher-order modes. We use two lens population models: the theory-based Press-Schechter halo mass function and an observation-based model derived from Sloan Digital Sky Survey. We find that the probability of detecting WO effects can be as large as $\sim 3\%$, $\sim1.5\%$, and $\sim 1 \%$ at $1\sigma$, $3\sigma$, and $5\sigma$ confidence levels, respectively. The most optimistic MBHB population model yields $\sim 8$, $\sim 4$, and $\sim 3$ events with detectable WO effects at the same confidence levels, while the rates drop to $\sim 0.01$ in the more pessimistic scenarios. The most likely lens masses probed by LISA are in the range $(10^3, 10^8)\, M_{\odot}$, and the most probable redshifts are in the range $(0.3, 1.7)$. Therefore, LISA observations of WO effects can probe low-mass DM halos, complementing strong lensing and other observations., Comment: 25 pages, 15 figures; matches the version published in Phys. Rev. D 108, 123543 (2023)

The population of binary black hole mergers observed in gravitational waves, together with astrophysical simulations, can help us to understand the properties of the progenitors and the binary formation mechanisms in different astrophysical scenarios. Here we focus on dynamical formation in star clusters. We use the third gravitational-wave transient catalog (GWTC-3) and Rapster, a rapid code to simulate cluster dynamics, to show that it is possible to construct the single-event likelihood of star cluster properties from individual observations. We find that the measured primary mass in a binary black hole merger correlates with the measured star cluster mass, because the mass spectrum of the primary component increases with the mass of the cluster. This trend may be caused by two physical mechanisms: (i) the more efficient production of hierarchical mergers with primary mass above $\sim 40~M_{\odot}$ for cluster masses of $\gtrsim 10^6~M_{\odot}$, and (ii) the suppression of more massive first-generation binaries, which happens because ejected binaries do not merge within the lookback time for cluster masses of $\lesssim 10^5~M_{\odot}$. The formalism presented here can be generalized to infer the population properties of binary progenitors in more realistic scenarios involving multiple formation channels., Comment: 5 pages, 3 figures. Calculations are shown in the python notebooks: https://gitlab.com/ken_ng/single-cluster-inference

Next-generation ground-based gravitational-wave observatories such as the Einstein Telescope and Cosmic Explorer will detect $O(10^{5}-10^{6})$ signals from compact binary coalescences every year, the exact number depending on uncertainties in the binary merger rate. Several overlapping signals will be present in band at any given time, generating a confusion noise background. We study how this confusion noise affects constraints on possible deviations from general relativity induced by modified gravity and environmental effects. Confusion noise impacts only the signals that last longer in band. Even for a "golden" GW170817-like signal, the constraints broaden by a factor in the range $[10\%,40\%]$ $([70\%,110\%])$ for the fiducial (highest) value of the local binary neutron star merger rate. Our ability to test general relativity or constrain environmental effects will be limited by systematic errors, and not by confusion noise., Comment: 11 pages, 5 figures

The current standard cosmological model is constructed within the framework of general relativity with a cosmological constant $\Lambda$, which is often associated with dark energy, and phenomenologically explains the accelerated cosmic expansion. Understanding the nature of dark energy is one of the most appealing questions in achieving a self-consistent physical model at cosmological scales. Modification of general relativity could potentially provide a more natural and physical solution to the accelerated expansion. The growth of the cosmic structure is sensitive in constraining gravity models. In this paper, we aim to provide a concise introductory review of modified gravity models from an observational point of view. We will discuss various mainstream cosmological observables, and their potential advantages and limitations as probes of gravity models., Comment: 72 pages, 19 figures, Invited review for Universe, Special Issue "Cosmological Constant"

We address two important questions in gravitational-wave astronomy. What is the astrophysical formation scenario leading to black-hole binary mergers? Did some of the merging black holes form hierarchically through previous generations of mergers? Leveraging fast-to-generate astrophysical simulations from the rapster code and a random forest algorithm, we develop a pipeline to accurately classify the most likely generation and formation scenario of dynamically formed BHs on an event-by-event basis. We test our framework on four merger events with features suggesting a dynamical origin: the large total mass event GW190521, GW190412 (with large mass asymmetry), and two events with effective spins antialigned with the orbital angular momentum (GW191109 and GW200225). Within the models we consider, and assuming these events to be formed dynamically, we find that one of the component black holes in GW190521 formed from a previous merger with high probability ($\gtrsim 85\%$). GW190521, GW191109 and GW200225 are compatible with formation through three-body interactions, while the most likely formation channel for GW190412 are two-body captures. We also rule out that GW191109 contains only first-generation black holes with a probability of 97$\%$. Our pipeline could be useful to identify the evolutionary path of individual GW observations once it is trained on more comprehensive sets of binary formation simulations., Comment: 9 pages, 2 figures. Public code at: https://github.com/aantonelli94/TheBHClassifier

We study scalar perturbations of topological solitons, smooth horizonless solutions in five-dimensional Einstein-Maxwell theory that correspond to coherent states of gravity via the dynamics of extra compact dimensions. First, we compute scalar quasinormal modes for topological stars that have a single unstable photon sphere, and we show that the spectrum is very similar to that of a black hole with the same photon sphere. Next, we study topological stars that have both a stable inner photon sphere and an unstable one. The first few quasinormal modes are localized around the inner photon sphere. The spectrum also contains ''black-hole like modes'' localized at the unstable outer photon sphere. The frequencies of these modes are similar to those of a black hole, but their imaginary part is smaller due to a cavity effect associated with the inner photon sphere. The longer damping produced by this trapping effect may have implications for black hole spectroscopy., Comment: 17 pages + Appendix, 11 figures

We use numerical simulations of scalar field dark matter evolving on a moving black hole background to confirm the regime of validity of (semi-)analytic expressions derived from first principles for both dynamical friction and momentum accretion in the relativistic regime. We cover both small and large clouds (relative to the de Broglie wavelength of the scalars), and light and heavy particle masses (relative to the BH size). In the case of a small dark matter cloud, the effect of accretion is a non-negligible contribution to the total force on the black hole, even for small scalar masses. We confirm that this momentum accretion transitions between two regimes (wave- and particle-like) and we identify the mass of the scalar at which the transition between regimes occurs., Comment: 11 pages, 5 figures. Minor corrections and references added to match published version

The addition of a Ricci coupling to Einstein-scalar-Gauss-Bonnet theories makes general relativity a cosmological attractor. Previous work considered a quadratic coupling function with two independent coupling constants in such theories and showed that static, spherically symmetric, spontaneously scalarized black holes are radially stable beyond a critical value of the Ricci coupling constant. Here we demonstrate that these black holes are affected by a quadrupole instability which leads to two new branches of static, axially symmetric scalarized black holes. We discuss the properties of these solutions and provide embedding diagrams., Comment: 5 pages, 4 figures

Galactic nuclei are potential hosts for intermediate-mass black holes (IMBHs), whose gravitational field can affect the motion of stars and compact objects. The absence of observable perturbations in our own Galactic Centre has resulted in a few constraints on the mass and orbit of a putative IMBH. Here, we show that the Laser Interferometer Space Antenna (LISA) can further constrain these parameters if the IMBH forms a binary with a compact remnant (a white dwarf, a neutron star, or a stellar-mass black hole), as the gravitational-wave signal from the binary will exhibit Doppler-shift variations as it orbits around Sgr A$^\star$. We argue that this method is the most effective for IMBHs with masses $10^3\,M_\odot\lesssim M_{\rm IMBH}\lesssim 10^5\,M_\odot$ and distances of $0.1$ mpc to $2$ mpc with respect to the supermassive black hole, a region of the parameter space partially unconstrained by other methods. We show that in this region the Doppler shift is most likely measurable whenever the binary is detected in the LISA band, and it can help constrain the mass and orbit of a putative IMBH in the centre of our Galaxy. We also discuss possible ways for an IMBH to form a binary in the Galactic Centre, showing that gravitational-wave captures of stellar-mass black holes and neutron stars are the most efficient channel., Comment: 9 pages, 4 figures. Accepted for publication in MNRAS

Black hole spectroscopy is the program to measure the complex gravitational-wave frequencies of merger remnants, and to quantify their agreement with the characteristic frequencies of black holes computed at linear order in black hole perturbation theory. In a "weaker" (non-agnostic) version of this test, one assumes that the frequencies depend on the mass and spin of the final Kerr black hole as predicted in perturbation theory. Linear perturbation theory is expected to be a good approximation only at late times, when the remnant is close enough to a stationary Kerr black hole. However, it has been claimed that a superposition of overtones with frequencies fixed at their asymptotic values in linear perturbation theory can reproduce the waveform strain even at the peak. Is this overfitting, or are the overtones physically present in the signal? To answer this question, we fit toy models of increasing complexity, waveforms produced within linear perturbation theory, and full numerical relativity waveforms using both agnostic and non-agnostic ringdown models. We find that higher overtones are unphysical: their role is mainly to "fit away" features such as initial data effects, power-law tails, and (when present) nonlinearities. We then identify physical quasinormal modes by fitting numerical waveforms in the original, agnostic spirit of the no-hair test. We find that a physically meaningful ringdown model requires the inclusion of higher multipoles, quasinormal mode frequencies induced by spherical-spheroidal mode mixing, and nonlinear quasinormal modes. Even in this "infinite signal-to-noise ratio" version of the original spectroscopy test, there is convincing evidence for the first overtone of the dominant multipole only well after the peak of the radiation., Comment: 52 pages (with a short executive summary), 33 figures, 1 table. Matches version published in PRD

We build an effective-one-body (EOB) Hamiltonian at third post-Newtonian (3PN) order in scalar-tensor (ST) and Einstein-scalar-Gauss-Bonnet (ESGB) theories of gravity. The latter is an extension of general relativity that predicts scalar hair for black holes. We start from the known two-body Lagrangian at 3PN order, and use order-reduction methods to construct its ordinary Hamiltonian counterpart. We then reduce the conservative two-body dynamics to the (nongeodesic) motion of a test particle in an effective metric by means of canonical transformations. The resulting EOB Hamiltonian is a modification of the general relativistic Hamiltonian, and already at 3PN order, it must account for nonlocal-in-time tail contributions. We include the latter beyond circular orbits and up to sixth order in the binary's orbital eccentricity. We finally calculate the orbital frequency at the innermost stable circular orbit (ISCO) of binary black holes in the shift-symmetric ESGB model. Our work extends F.L. Juli\'e and N. Deruelle [Phys. Rev. D 95, 124054 (2017)], and it is an essential step toward the accurate modeling of gravitational waveforms beyond general relativity., Comment: Minor changes to match published version. Results unchanged

Nuclear star clusters, which fragment into metal-poor stars in situ at the centers of protogalaxies, provide ideal environments for the formation of intermediate-mass black holes with masses $10^3-10^6M_\odot$. We utilize the semianalytic model implemented in Rapster, a public rapid cluster evolution code. We implement simple recipes for stellar collisions and gas accretion/expulsion into the code and identify the regimes where each channel contributes to the dynamical formation of intermediate-mass black holes via repeated mergers of stellar black hole seeds. We find that intermediate-mass black hole formation in gas-rich environments is almost inevitable if the initial mean density of the nuclear cluster is $>10^8M_\odot\,{\rm pc}^{-3}$. A million solar mass black hole can form within 100~Myr in the heaviest ($>10^7M_\odot$) and most compact ($<0.5~{\rm pc}$) nuclear clusters. We demonstrate that by today these resemble the observed range of nuclear clusters in dwarf galaxies and that there are potential gravitational-wave signatures of the massive black hole formation process., Comment: 13 pages, 7 figures, matches published version

We study photon geodesics in topological solitons that have the same asymptotic properties as Schwarzschild black holes. These are coherent states in string theory corresponding to pure deformations of spacetime through the dynamics of compact extra dimensions. We compare these solutions with Schwarzschild black holes by computing null geodesics, deriving Lyapunov exponents, and imaging their geometries as seen by a distant observer. We show that topological solitons are remarkably similar to black holes in apparent size and scattering properties, while being smooth and horizonless. Incoming photons experience very high redshift, inducing phenomenological horizon-like behaviors from the point of view of photon scattering. Thus, they provide a compelling case for real-world gravitational solitons and topological alternatives to black holes from string theory., Comment: 15 pages and 6 figures, v2: typos corrected, v3: minor changes and published version

The accumulation of certain types of dark matter particles in neutron star cores due to accretion over long timescales can lead to the formation of a mini black hole. In this scenario, the neutron star is destabilized and implodes to form a black hole without significantly increasing its mass. When this process occurs in neutron stars in coalescing binaries, one or both stars might be converted to a black hole before they merge. Thus, in the mass range of $\sim \mbox{1--2}\, M_\odot,$ the Universe might contain three distinct populations of compact binaries: one containing only neutron stars, the second population of only black holes, and a third, mixed population consisting of a neutron star and a black hole. However, it is unlikely to have a mixed population as the various timescales allow for both neutron stars to remain or collapse within a short timescale. In this paper, we explore the capability of future gravitational-wave detector networks, including upgrades of Advanced LIGO and Virgo, and new facilities such as the Cosmic Explorer and Einstein Telescope (XG network), to discriminate between different populations by measuring the effective tidal deformability of the binary, which is zero for binary black holes but nonzero for binary neutron stars. Furthermore, we show that observing the relative abundances of the different populations can be used to infer the timescale for neutron stars to implode into black holes, and in turn, provide constraints on the particle nature of dark matter. The XG network will infer the implosion timescale to within an accuracy of 0.01 Gyr at 90% credible interval and determine the dark matter mass and interaction cross section to within a factor of 2 GeV and 10 cm$^{-2}$, respectively.

Gravitational-wave observations have just started probing the properties of black hole binary merger populations. The observation of binaries with very massive black holes and significantly asymmetric masses motivates the study of dense star clusters as astrophysical environments which can produce such events dynamically. In this paper we present Rapster (for "Rapid cluster evolution"), a new code designed to rapidly model binary black hole population synthesis and the evolution of massive star clusters based on simple, yet realistic prescriptions. We also perform a thorough comparison with the Cluster Monte Carlo code and find generally good agreement. The code can be used to generate large populations of dynamically formed binary black holes., Comment: 34 pages, 10 figures, 1 table. Manuscript and code were significantly revised in response to the referees' comments. Matches the published version. The Rapster code and data are publicly available at https://github.com/Kkritos/Rapster and https://zenodo.org/records/10626210

In a General Relativistic framework, Gravitational Waves (GW) and Electromagnetic (EM) waves are expected to respond in the same way to the effects of matter perturbations between the emitter and the observer. A different behaviour might be a signature of alternative theories of gravity. In this work we study the cross-correlation of resolved GW events (from compact objects mergers detected by the Einstein Telescope, either assuming or excluding the detection of an EM counterpart) and EM signals (coming both from the Intensity Mapping of the neutral hydrogen distribution and resolved galaxies from the SKA Observatory), considering weak lensing, angular clustering and their cross term ($\mathrm{L \times C}$) as observable probes. Cross-correlations of these effects are expected to provide promising information on the behaviour of these two observables, hopefully shedding light on beyond GR signatures. We perform a Fisher matrix analysis with the aim of constraining the $\{\mu_0,\eta_0,\Sigma_0\}$ parameters, either opening or keeping fixed the background parameters $\{w_0,w_a\}$. We find that, although lensing-only forecasts provide significantly unconstrained results, the combination with angular clustering and the cross-correlation of all three considered tracers (GW, IM, resolved galaxies) leads to interesting and competitive constraints. This offers a novel and alternative path to both multi-tracing opportunities for Cosmology and the Modified Gravity sector., Comment: 36 pages, 13 figures, 4 tables. Matches the published version

Next-generation terrestrial gravitational-wave observatories will detect $\mathcal{O}(10^{5})$ signals from compact binary coalescences every year. These signals can last for several hours in the detectors' sensitivity band and they will be affected by multiple unresolved sources contributing to a confusion-noise background in the data. Using an information-matrix formalism, we estimate the impact of the confusion noise power spectral density in broadening the parameter estimates of a GW170817-like event. If our estimate of the confusion noise power spectral density is neglected, we find that masses, spins, and distance are biased in about half of our simulations under realistic circumstances. The sky localization, while still precise, can be biased in up to $80\%$ of our simulations, potentially posing a problem in follow-up searches for electromagnetic counterparts., Comment: 6 pages, 2 figures

In modified theories of gravity, the potentials appearing in the Schr\"odinger-like equations that describe perturbations of non-rotating black holes are also modified. In this paper we ask: can these modifications be constrained with high-precision gravitational-wave measurements of the black hole's quasinormal mode frequencies? We expand the modifications in a small perturbative parameter regulating the deviation from the general-relativistic potential, and in powers of $M/r$. We compute the quasinormal modes of the modified potential up to quadratic order in the perturbative parameter. Then we use Markov-chain-Monte-Carlo (MCMC) methods to recover the coefficients in the $M/r$ expansion in an ``optimistic'' scenario where we vary them one at a time, and in a ``pessimistic'' scenario where we vary them all simultaneously. In both cases, we find that the bounds on the individual parameters are not robust. Because quasinormal mode frequencies are related to the behavior of the perturbation potential near the light ring, we propose a different strategy. Inspired by Wentzel-Kramers-Brillouin (WKB) theory, we demonstrate that the value of the potential and of its second derivative at the light ring can be robustly constrained. These constraints allow for a more direct comparison between tests based on black hole spectroscopy and observations of black hole `shadows'' by the Event Horizon Telescope and future instruments., Comment: 12 pages, 7 figures

Current prescriptions for supernova natal kicks in rapid binary population synthesis simulations are based on fits of simple functions to single pulsar velocity data. We explore a new parameterization of natal kicks received by neutron stars in isolated and binary systems developed by Mandel & M\"uller, which is based on 1D and 3D supernova simulations and accounts for the physical correlations between progenitor properties, remnant mass, and the kick velocity. We constrain two free parameters in this model using very long baseline interferometry velocity measurements of Galactic single pulsars. We find that the inferred values of natal kick parameters do not differ significantly between single and binary evolution scenarios. The best-fit values of these parameters are $v_{\rm ns} = 520$ km s$^{-1}$ for the scaling pre-factor for neutron star kicks, and $\sigma_{\rm ns}=0.3$ for the fractional stochastic scatter in the kick velocities., Comment: 8 pages, 8 figures, 1 table. Updated to match MNRAS version

Stochastic gravitational-wave backgrounds (SGWBs) derive from the superposition of numerous individually unresolved gravitational-wave (GW) signals. Detecting SGWBs provides us with invaluable information about astrophysics, cosmology, and fundamental physics. In this paper, we study SGWBs from binary black-hole (BBH) and binary neutron-star (BNS) coalescences in a network of next-generation ground-based GW observatories (Cosmic Explorer and Einstein Telescope) and determine how well they can be measured; this then limits how well we can observe other subdominant astrophysical and cosmological SGWBs. We simulate all-Universe populations of BBHs and BNSs and calculate the corresponding SGWBs, which consist of a superposition of (i) undetected signals, and (ii) the residual background from imperfect removal of resolved sources. The sum of the two components sets the sensitivity for observing other SGWBs. Our results show that, even with next-generation observatories, the residual background is large and limits the sensitivity to other SGWBs. The main contributions to the residual background arise from uncertainties in inferring the coalescence phase and luminosity distance of the detected signals. Alternative approaches to signal subtraction would need to be explored to minimize the BBH and BNS foreground in order to observe SGWBs from other subdominant astrophysical and cosmological sources., Comment: 19 pages, 10 figures, matches the published version

The stochastic gravitational-wave backgrounds (SGWBs) for current detectors are dominated by binary black-hole (BBH) and binary neutron-star (BNS) coalescences. The sensitivity of current networks of gravitational-wave (GW) detectors allows only a small fraction of BBHs and BNSs to be resolved and subtracted, but previous work indicated that the situation should significantly improve with next-generation (XG) observatories. We revisit these conclusions by taking into account waveform-modeling uncertainties, updated astrophysical models, and (crucially) the full set of parameters that must be estimated to remove the resolved sources. Compared to previous studies, we find that the residual background from BBHs and BNSs is large even with XG detector networks. New data analysis methods will thus be required to observe the SGWB from cosmic supernovae or contributions from early-Universe phenomena like cosmic strings, stiff post-inflation fluids, or axion inflation., Comment: 6 pages, 2 figures

We report evidence for nonlinear modes in the ringdown stage of the gravitational waveform produced by the merger of two comparable-mass black holes. We consider both the coalescence of black hole binaries in quasicircular orbits and high-energy, head-on black hole collisions. The presence of nonlinear modes in the numerical simulations confirms that general-relativistic nonlinearities are important and must be considered in gravitational-wave data analysis., Comment: 6 + 6 pages, 7 figures. Matches version published in Physical Review Letters

The gravitational waves emitted by massive black hole binaries in the LISA band can be lensed. Wave-optics effects in the lensed signal are crucial when the Schwarzschild radius of the lens is smaller than the wavelength of the radiation. These frequency-dependent effects can enable us to infer the lens parameters, possibly with a single detection alone. In this work, we assess the observability of wave-optics effects with LISA by performing an information-matrix analysis using analytical solutions for both point-mass and singular isothermal sphere lenses. We use gravitational-waveform models that include the merger, ringdown, higher harmonics, and aligned spins to study how waveform models and source parameters affect the measurement errors in the lens parameters. We find that previous work underestimated the observability of wave-optics effects and that LISA can detect lensed signals with higher impact parameters and lower lens masses., Comment: 18 pages, 9 figures; matches the version published in Phys. Rev. D 107, 043029 (2023)