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The Simulating eXtreme Spacetimes Collaboration's code SpEC can now routinely simulate binary black hole mergers undergoing $\sim25$ orbits, with the longest simulations undergoing nearly $\sim180$ orbits. While this sounds impressive, the mismatch between the highest resolutions for this long simulation is $\mathcal{O}(10^{-1})$. Meanwhile, the mismatch between resolutions for the more typical simulations tends to be $\mathcal{O}(10^{-4})$, despite the resolutions being similar to the long simulations'. In this note, we explain why mismatch alone gives an incomplete picture of code -- and waveform -- quality, especially in the context of providing waveform templates for LISA and 3G detectors, which require templates with $\mathcal{O}(10^{3}) - \mathcal{O}(10^{5})$ orbits. We argue that to ready the GW community for the sensitivity of future detectors, numerical relativity groups must be aware of this caveat, and also run future simulations with at least three resolutions to properly assess waveform accuracy., Comment: 8 pages, 2 figures

We uncover late-time gravitational-wave tails in fully nonlinear 3+1 dimensional numerical relativity simulations of merging black holes, using the highly accurate SpEC code. We achieve this result by exploiting the strong magnification of late-time tails due to binary eccentricity, recently observed in perturbative evolutions, and showcase here the tail presence in head-on configurations for several mass ratios close to unity. We validate the result through a large battery of numerical tests and detailed comparison with perturbative evolutions, which display striking agreement with full nonlinear ones. Our results offer yet another confirmation of the highly predictive power of black hole perturbation theory in the presence of a source, even when applied to nonlinear solutions. The late-time tail signal is much more prominent than anticipated until recently, and possibly within reach of gravitational-wave detectors measurements, unlocking observational investigations of an additional set of general relativistic predictions on the long-range gravitational dynamics., Comment: 5+7 pages, 2+5 figures, 1+1 tables

The motion of compact binaries is influenced by the spin of their components starting at the 1.5 post-Newtonian (PN) order. On the other hand, in the large mass ratio limit, the spin of the lighter object appears in the equations of motion at first order in the mass ratio, coinciding with the leading gravitational self-force. Frame and gauge choices make it challenging to compare between the two limits, especially for generic spin configurations. We derive novel closed formulas for the gauge-invariant actions and frequencies for the motion of spinning test particles near Kerr black holes. We use this to express the Hamiltonian perturbatively in terms of action variables up to 3PN and compare it with the 1.5 PN action-angle Hamiltonian at finite mass ratios. This allows us to match the actions across both systems, providing a new gauge-invariant dictionary for interpolation between the two limits., Comment: Supplemental notebook with actions and frequencies for the spinning particle and the 3PN expansions in "Ancillary files"

The inspiral of a circular, non-precessing binary exhibits an approximate helical symmetry. The effects of eccentricity, precession, and radiation reaction break the exact symmetry. We estimate the failure of this symmetry using the flux of the BMS charge corresponding to helical symmetry carried away by gravitational waves. We analytically compute the helical flux for binaries moving on eccentric orbits and quasi-circular orbits without precession using post-Newtonian theory. The helical flux is non-vanishing at the 0PN order for eccentric orbits as expected. We analytically predict the helical flux to be at a relative 5PN order for quasi-circular non-precessing binaries. This prediction is compared with 113 quasi-circular non-precessing numerical relativity waveforms from the SXS catalog. We find good agreement between analytical and numerical results for quasi-circular non-precessing binaries establishing that helical symmetry starts to break at 5PN for these binaries., Comment: 9+1 pages, 4 figures. Comments welcome

The increasing adoption of Deep Neural Network (DNN)-based Digital Pre-distortion (DPD) in modern communication systems necessitates efficient hardware implementations. This paper presents DPD-NeuralEngine, an ultra-fast, tiny-area, and power-efficient DPD accelerator based on a Gated Recurrent Unit (GRU) neural network (NN). Leveraging a co-designed software and hardware approach, our 22 nm CMOS implementation operates at 2 GHz, capable of processing I/Q signals up to 250 MSps. Experimental results demonstrate a throughput of 256.5 GOPS and power efficiency of 1.32 TOPS/W with DPD linearization performance measured in Adjacent Channel Power Ratio (ACPR) of -45.3 dBc and Error Vector Magnitude (EVM) of -39.8 dB. To our knowledge, this work represents the first AI-based DPD application-specific integrated circuit (ASIC) accelerator, achieving a power-area efficiency (PAE) of 6.6 TOPS/W/mm$^2$., Comment: This paper has been accepted to be presented at the 2025 International Symposium on Circuits and Systems (ISCAS)

Highly precise and robust waveform models are required as improvements in detector sensitivity enable us to test general relativity with more precision than ever before. In this work, we introduce a spin-aligned surrogate ringdown model. This ringdown surrogate, NRSur3dq8_RD, is built with numerical waveforms produced using Cauchy-characteristic evolution. In addition, these waveforms are in the superrest frame of the remnant black hole allowing us to do a correct analysis of the ringdown spectrum. The novel prediction of our surrogate model is complex-valued quasinormal mode (QNM) amplitudes, with median relative errors of $10^{-2}-10^{-3}$ over the parameter space. Like previous remnant surrogates, we also predict the remnant black hole's mass and spin. The QNM mode amplitude errors translate into median errors on ringdown waveforms of $10^{-4}$. The high accuracy and QNM mode content provided by our surrogate will enable high-precision ringdown analyses such as tests of general relativity. Our ringdown model is publicly available through the python package surfinBH., Comment: 11+2 pages, 13 figures, 1 table. This new model is publicly available through surfinBH https://pypi.org/project/surfinBH/

Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our universe., Comment: 22 pages, 8 figures. Matches published version in CGQ's focus issue: Gravitational-Wave Memory Effects: From Theory to Observation

Digital Pre-Distortion (DPD) enhances signal quality in wideband RF power amplifiers (PAs). As signal bandwidths expand in modern radio systems, DPD's energy consumption increasingly impacts overall system efficiency. Deep Neural Networks (DNNs) offer promising advancements in DPD, yet their high complexity hinders their practical deployment. This paper introduces open-source mixed-precision (MP) neural networks that employ quantized low-precision fixed-point parameters for energy-efficient DPD. This approach reduces computational complexity and memory footprint, thereby lowering power consumption without compromising linearization efficacy. Applied to a 160MHz-BW 1024-QAM OFDM signal from a digital RF PA, MP-DPD gives no performance loss against 32-bit floating-point precision DPDs, while achieving -43.75 (L)/-45.27 (R) dBc in Adjacent Channel Power Ratio (ACPR) and -38.72 dB in Error Vector Magnitude (EVM). A 16-bit fixed-point-precision MP-DPD enables a 2.8X reduction in estimated inference power. The PyTorch learning and testing code is publicly available at \url{https://github.com/lab-emi/OpenDPD}., Comment: Accepted to IEEE Microwave and Wireless Technology Letters (MWTL)

We numerically investigate the imprints of gravitational radiation-reaction driven changes to a black hole's mass and spin on the corresponding ringdown waveform. We do so by comparing the dynamics of a perturbed black hole evolved with the full (nonlinear) versus linearized Einstein equations. As expected, we find that the quasinormal mode amplitudes extracted from nonlinear evolution deviate from their linear counterparts at third order in initial perturbation amplitude. For perturbations leading to a change in the black hole mass and spin of $\sim 5\%$, which is reasonable for a remnant formed in an astrophysical merger, we find that nonlinear distortions to the complex amplitudes of some quasinormal modes can be as large as $\sim 50\%$ at the peak of the waveform. Furthermore, the change in the mass and spin results in a drift in the quasinormal mode frequencies, which for large amplitude perturbations causes the nonlinear waveform to rapidly dephase with respect to its linear counterpart. %These two nonlinear effects together create a large distortion in both the amplitude and phase of the ringdown gravitational waveform. Surprisingly, despite these nonlinear effects creating significant deviations in the nonlinear waveform, we show that a linear quasinormal mode model still performs quite well from close to the peak amplitude onwards.

In this short Note, I answer the titular question: Yes, a radiation gauge can be horizon-locking. Radiation gauges are very common in black hole perturbation theory. It's also very convenient if a gauge choice is horizon-locking, i.e. the location of the horizon is not moved by a linear metric perturbation. Therefore it is doubly convenient that a radiation gauge can be horizon-locking, when some simple criteria are satisfied. Though the calculation is straightforward, it seemed useful enough to warrant writing this Note. Finally I show an example: the $\ell$ vector of the Hartle-Hawking tetrad in Kerr satisfies all the conditions for ingoing radiation gauge to keep the future horizon fixed., Comment: 5+1 pages, comments welcome. v2: Matches version published to CQG

While the rise of large language models (LLMs) has created rich new opportunities to learn about digital technology, many on the margins of this technology struggle to gain and maintain competency due to lexical or conceptual barriers that prevent them from asking appropriate questions. Although there have been many efforts to understand factuality of LLM-created content and ability of LLMs to answer questions, it is not well understood how unclear or nonstandard language queries affect the model outputs. We propose the creation of a dataset that captures questions of digital newcomers and outsiders, utilizing data we have compiled from a decade's worth of one-on-one tutoring. In this paper we lay out our planned efforts and some potential uses of this dataset., Comment: Presented at the AI4ED workshop at AAAI 2024

Like light, gravitational waves can be gravitationally lensed by massive astrophysical objects. For galaxy and galaxy-cluster lenses, one expects to see strong lensing -- forecasted to become observable in the coming years -- where the original wave is split into multiple copies with the same frequency evolution but different overall arrival times, phases, amplitudes, and signal strengths. Some of these images can be below the detection threshold and require targeted search methods, based on tailor-made template banks. These searches can be made more sensitive by using our knowledge of the typical distribution and morphology of lenses to predict the time delay, magnification, and image-type ordering of the lensed images. Here, we show that when a subset of the images is super-threshold, they can be used to construct a more constrained prediction of the arrival time of the remaining signals, enhancing our ability to identify lensing candidate signals. Our suggested method effectively reduces the list of triggers requiring follow-up and generally re-ranks the genuine counterpart higher in the lensing candidate list. Therefore, in the future, if one observes two or three lensed images, the information they provide can be used to identify their sub-threshold counterparts, thus allowing identification of additional lensed images. Finding such images would also strengthen our evidence for the event being lensed., Comment: 15 pages, 28 figures, 1 table

Numerical relativity (NR) simulations of binary black holes provide precise waveforms, but are typically too computationally expensive to produce waveforms with enough orbits to cover the whole frequency band of gravitational-wave observatories. Accordingly, it is important to be able to hybridize NR waveforms with analytic, post-Newtonian (PN) waveforms, which are accurate during the early inspiral phase. We show that to build such hybrids, it is crucial to both fix the Bondi-Metzner-Sachs (BMS) frame of the NR waveforms to match that of PN theory, and optimize over the PN parameters. We test such a hybridization procedure including all spin-weighted spherical harmonic modes with $|m|\leq \ell$ for $\ell\leq 8$, using 29 NR waveforms with mass ratios $q\leq 10$ and spin magnitudes $|\chi_1|, |\chi_2|\leq 0.8$. We find that for spin-aligned systems, the PN and NR waveforms agree very well. The difference is limited by the small nonzero orbital eccentricity of the NR waveforms, or equivalently by the lack of eccentric terms in the PN waveforms. To maintain full accuracy of the simulations, the matching window for spin-aligned systems should be at least 5 orbits long and end at least 15 orbits before merger. For precessing systems, the errors are larger than for spin-aligned cases. The errors are likely limited by the absence of precession-related spin-spin PN terms. Using $10^5\,M$ long NR waveforms, we find that there is no optimal choice of the matching window within this time span, because the hybridization result for precessing cases is always better if using earlier or longer matching windows. We provide the mean orbital frequency of the smallest acceptable matching window as a function of the target error between the PN and NR waveforms and the black hole spins., Comment: 21 pages, 22 figures

With the rise in communication capacity, deep neural networks (DNN) for digital pre-distortion (DPD) to correct non-linearity in wideband power amplifiers (PAs) have become prominent. Yet, there is a void in open-source and measurement-setup-independent platforms for fast DPD exploration and objective DPD model comparison. This paper presents an open-source framework, OpenDPD, crafted in PyTorch, with an associated dataset for PA modeling and DPD learning. We introduce a Dense Gated Recurrent Unit (DGRU)-DPD, trained via a novel end-to-end learning architecture, outperforming previous DPD models on a digital PA (DPA) in the new digital transmitter (DTX) architecture with unconventional transfer characteristics compared to analog PAs. Measurements show our DGRU-DPD achieves an ACPR of -44.69/-44.47 dBc and an EVM of -35.22 dB for 200 MHz OFDM signals. OpenDPD code, datasets, and documentation are publicly available at https://github.com/lab-emi/OpenDPD., Comment: To be published at the 2024 IEEE International Symposium on Circuits and Systems (ISCAS), Singapore

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

Numerical relativity simulations provide the most precise templates for the gravitational waves produced by binary black hole mergers. However, many of these simulations use an incomplete waveform extraction technique -- extrapolation -- that fails to capture important physics, such as gravitational memory effects. Cauchy-characteristic evolution (CCE), by contrast, is a much more physically accurate extraction procedure that fully evolves Einstein's equations to future null infinity and accurately captures the expected physics. In this work, we present a new surrogate model, NRHybSur3dq8$\_$CCE, built from CCE waveforms that have been mapped to the post-Newtonian (PN) BMS frame and then hybridized with PN and effective one-body (EOB) waveforms. This model is trained on 102 waveforms with mass ratios $q\leq8$ and aligned spins $\chi_{1z}, \, \chi_{2z} \in \left[-0.8, 0.8\right]$. The model spans the entire LIGO-Virgo-KAGRA (LVK) frequency band (with $f_{\text{low}}=20\text{Hz}$) for total masses $M\gtrsim2.25M_{\odot}$ and includes the $\ell\leq4$ and $(\ell,m)=(5,5)$ spin-weight $-2$ spherical harmonic modes, but not the $(3,1)$, $(4,2)$ or $(4,1)$ modes. We find that NRHybSur3dq8$\_$CCE can accurately reproduce the training waveforms with mismatches $\lesssim2\times10^{-4}$ for total masses $2.25M_{\odot}\leq M\leq300M_{\odot}$ and can, for a modest degree of extrapolation, capably model outside of its training region. Most importantly, unlike previous waveform models, the new surrogate model successfully captures memory effects., Comment: 14 pages, 11 figures. Accepted for publication in PRD

We present a numerical-relativity simulation of a black hole - neutron star merger in scalar-tensor (ST) gravity with binary parameters consistent with the gravitational wave event GW200115. In this exploratory simulation, we consider the Damour-Esposito-Farese extension to Brans-Dicke theory, and maximize the effect of spontaneous scalarization by choosing a soft equation of state and ST theory parameters at the edge of known constraints. We extrapolate the gravitational waves, including tensor and scalar (breathing) modes, to future null-infinity. The numerical waveforms undergo ~ 22 wave cycles before the merger, and are in good agreement with predictions from post-Newtonian theory during the inspiral. We find the ST system evolves faster than its general-relativity (GR) counterpart due to dipole radiation, merging a full gravitational-wave cycle before the GR counterpart. This enables easy differentiation between the ST waveforms and GR in the context of parameter estimation. However, we find that dipole radiation's effect may be partially degenerate with the NS tidal deformability during the late inspiral stage, and a full Bayesian analysis is necessary to fully understand the degeneracies between ST and binary parameters in GR.

Optimization of strongly non-linear tightly coupled feeds attached to antennas is a challenging problem from a purely computational perspective. One can imagine that an optimization would (a) need to be in the time domain, and (b) has to be self-consistently coupled with the linear antenna (or electromagnetic) system. These two imply that the cost of optimization is governed by the need to repeatedly evaluate the fully coupled cost function. This paper leverages a recently developed transient port-extraction technique to circumvent this challenge and is agnostic to the optimization scheme. This approach provides a representation of the entire linear electromagnetic system at the port and can readily integrate with any non-linear circuit analysis and optimization methodology. In this paper, we demonstrate optimization of linear and non-linear circuit feed parameters that are tightly coupled to broadband radiating systems., Comment: 4 pages, 7 figures

The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers, in large part, due to the method strictly following the proper space for representing fields, charges, and measuring currents. Unfortunately, leap-frog based solvers (and their other incarnations) are only conditionally stable. Recent advances have made Electromagnetic Finite Element Particle-in-Cell (EM-FEMPIC) methods built around unconditionally stable time stepping schemes were shown to conserve charge. Together with the use of a quasi-Helmholtz decomposition, these methods were both unconditionally stable and satisfied Gauss' Laws to machine precision. However, this architecture was developed for systems with explicit particle integrators where fields and velocities were off by a time step. While completely self-consistent methods exist in the literature, they follow the classic rubric: collect a system of first order differential equations (Maxwell and Newton equations) and use an integrator to solve the combined system. These methods suffer from the same side-effect as earlier--they are conditionally stable. Here we propose a different approach; we pair an unconditionally stable Maxwell solver to an exponential predictor-corrector method for Newton's equations. As we will show via numerical experiments, the proposed method conserves energy within a PIC scheme, has an unconditionally stable EM solve, solves Newton's equations to much higher accuracy than a traditional Boris solver and conserves charge to machine precision. We further demonstrate benefits compared to other polynomial methods to solve Newton's equations, like the well known Boris push., Comment: 12 pages, 15 figures

The closed-form solution of the 1.5 post-Newtonian (PN) accurate binary black hole (BBH) Hamiltonian system has proven to be difficult to obtain for a long time since its introduction in 1966. Closed-form solutions of the PN BBH systems with arbitrary parameters (masses, spins, eccentricity) are required for modeling the gravitational waves (GWs) emitted by them. Accurate models of GWs are crucial for their detection by LIGO/Virgo and LISA. Only recently, two solution methods for solving the BBH dynamics were proposed in arXiv:1908.02927 (without using action-angle variables), and arXiv:2012.06586, arXiv:2110.15351 (action-angle based). This paper combines the ideas laid out in the above articles, fills the missing gaps and provides the two solutions which are fully 1.5PN accurate. We also present a public Mathematica package BBHpnToolkit which implements these two solutions and compares them with a fully numerical treatment. The level of agreement between these solutions provides a numerical verification for all the five actions constructed in arXiv:2012.06586, and arXiv:2110.15351. This paper hence serves as a stepping stone for pushing the action-angle-based solution to 2PN order via canonical perturbation theory., Comment: (2+15) pages, (1+4) figures. This version is composed of an erratum (wrt. the previous arXiv preprint version), and the fully revised article appended thereafter

The gravitational wave strain emitted by a perturbed black hole (BH) ringing down is typically modeled analytically using first-order BH perturbation theory. In this Letter we show that second-order effects are necessary for modeling ringdowns from BH merger simulations. Focusing on the strain's $(\ell,m)=(4,4)$ angular harmonic, we show the presence of a quadratic effect across a range of binary BH mass ratios that agrees with theoretical expectations. We find that the quadratic $(4,4)$ mode's amplitude exhibits quadratic scaling with the fundamental $(2,2)$ mode -- its parent mode. The nonlinear mode's amplitude is comparable to or even larger than that of the linear $(4,4)$ mode. Therefore, correctly modeling the ringdown of higher harmonics -- improving mode mismatches by up to 2 orders of magnitude -- requires the inclusion of nonlinear effects., Comment: 6+2 pages, 4 figures, 1 table. Matches PRL version

The Bondi-van der Burg-Metzner-Sachs (BMS) group, which uniquely describes the symmetries of asymptotic infinity and therefore of the gravitational waves that propagate there, has become increasingly important for accurate modeling of waveforms. In particular, waveform models, such as post-Newtonian (PN) expressions, numerical relativity (NR), and black hole perturbation theory, produce results that are in different BMS frames. Consequently, to build a model for the waveforms produced during the merging of compact objects, which ideally would be a hybridization of PN, NR, and black hole perturbation theory, one needs a fast and robust method for fixing the BMS freedoms. In this work, we present the first means of fixing the entire BMS freedom of NR waveforms to match the frame of either PN waveforms or black hole perturbation theory. We achieve this by finding the BMS transformations that change certain charges in a prescribed way -- e.g., finding the center-of-mass transformation that maps the center-of-mass charge to a mean of zero. We find that this new method is 20 times faster, and more correct when mapping to the superrest frame, than previous methods that relied on optimization algorithms. Furthermore, in the course of developing this charge-based frame fixing method, we compute the PN expression for the Moreschi supermomentum to 3PN order without spins and 2PN order with spins. This Moreschi supermomentum is effectively equivalent to the energy flux or the null memory contribution at future null infinity $\mathscr{I}^{+}$. From this PN calculation, we also compute oscillatory ($m\not=0$ modes) and spin-dependent memory terms that have not been identified previously or have been missing from strain expressions in the post-Newtonian literature., Comment: 16+4 pages with 2 appendices, 4 figures, 1 table

One of the key ingredients for making binary waveform predictions in a beyond-GR theory of gravity is understanding the energy and angular momentum carried by gravitational waves and any other radiated fields. Identifying the appropriate energy functional is unclear in Hassan-Rosen bigravity, a ghost-free theory with one massive and one massless graviton. The difficulty arises from the new degrees of freedom and length scales which are not present in GR, rendering an Isaacson-style averaging calculation ambiguous. In this article we compute the energy carried by gravitational waves in bigravity starting from the action, using the canonical current formalism. The canonical current agrees with other common energy calculations in GR, and is unambiguous (modulo boundary terms), making it a convenient choice for quantifying the energy of gravitational waves in bigravity or any diffeomorphism-invariant theories of gravity. This calculation opens the door for future waveform modeling in bigravity to correctly include backreaction due to emission of gravitational waves., Comment: 18+4 pages, 2 figures; v2: fixed typos and added references, matches published version

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., Comment: Accepted in: Living Reviews in Relativity

One of the important targets for the future space-based gravitational wave observatory LISA is extreme mass ratio inspirals (EMRIs), where long and accurate waveform modeling is necessary for detection and characterization. Modeling EMRI dynamics requires accounting for effects such as the ones induced by an external tidal field, which can break integrability at resonances and cause significant dephasing. In this paper, we use a Newtonian analogue of a Kerr black hole to study the effect of an external tidal field on the dynamics and the gravitational waveform. We have developed a numerical framework that takes advantage of the integrability of the background system to evolve it with a symplectic splitting integrator, and compute approximate gravitational waveforms to estimate the timescale over which the perturbation affects the dynamics. Comparing this timescale with the characteristic time under radiation reaction at resonance, we introduce a tool for quantifying the regime in which tidal effects might be included when modeling EMRI gravitational waves. As an application of this framework, we perform a detailed analysis of the dynamics at one resonance to show how different entry points into the resonance in phase-space can produce substantially different dynamics, and how one can estimate bounds for the parameter space where tidal effects may become dominant. Such bounds will scale as $\varepsilon \gtrsim C \, q$, where $\varepsilon$ measures the strength of the external tidal field, $q$ is the mass ratio, and $C$ is a number which depends on the resonance and the shape of the tide. We demonstrate how to estimate $C$ using our framework for the 2:3 radial to polar frequency resonance in our model system. This framework can serve as a proxy for proper modeling of the tidal perturbation in the fully relativistic case., Comment: V2. Updated to match published version

Quasi-normal mode (QNM) modeling is an invaluable tool for characterizing remnant black holes, studying strong gravity, and testing GR. Only recently have QNM studies begun to focus on multimode fitting to numerical relativity (NR) strain waveforms. As GW observatories become even more sensitive they will be able to resolve higher-order modes. Consequently, multimode QNM fits will be critically important, and in turn require a more thorough treatment of the asymptotic frame at $\mathscr{I}^+$. The first main result of this work is a method for systematically fitting a QNM model containing many modes to a numerical waveform produced using Cauchy-characteristic extraction (CCE), an extraction technique which is known to resolve memory effects. We choose the modes to model based on their power contribution to the residual between numerical and model waveforms. We show that the all-mode strain mismatch improves by a factor of $\sim10^5$ when using multimode fitting as opposed to only fitting the $(2,\pm2,n)$ modes. Our most significant result addresses a critical point that has been overlooked in the QNM literature: the importance of matching the Bondi-van der Burg-Metzner-Sachs (BMS) frame of the numerical waveform to that of the QNM model. We show that by mapping the numerical waveforms$-$which exhibit the memory effect$-$to a BMS frame known as the super rest frame, there is an improvement of $\sim10^5$ in the all-mode strain mismatch compared to using a strain waveform whose BMS frame is not fixed. Furthermore, we find that by mapping CCE waveforms to the super rest frame, we can obtain all-mode mismatches that are, on average, a factor of $\sim4$ better than using the publicly-available extrapolated waveforms. We illustrate the effectiveness of these modeling enhancements by applying them to families of waveforms produced by NR and comparing our results to previous QNM studies., Comment: 17 + 2 pages, 11 figures, 2 tables

Accurate and efficient modeling of the dynamics of binary black holes (BBHs) is crucial to their detection through gravitational waves (GWs), with LIGO/Virgo/KAGRA, and LISA in the future. Solving the dynamics of a BBH system with arbitrary parameters without simplifications (like orbit- or precession-averaging) in closed form is one of the most challenging problems for the GW community. One potential approach is using canonical perturbation theory which constructs perturbed action-angle variables from the unperturbed ones of an integrable Hamiltonian system. Having action-angle variables of the integrable 1.5 post-Newtonian (PN) BBH system is therefore imperative. In this paper, we continue the work initiated by two of us in arXiv:2012.06586, where we presented four out of five actions of a BBH system with arbitrary eccentricity, masses, and spins, at 1.5PN order. Here we compute the remaining fifth action using a novel method of extending the phase space by introducing unmeasurable phase space coordinates. We detail how to compute all the frequencies, and sketch how to explicitly transform from the action-angle variables to the usual positions and momenta. This analytically solves the dynamics at 1.5PN. This lays the groundwork to analytically solve the conservative dynamics of the BBH system with arbitrary masses, spins, and eccentricity, at higher PN order, by using canonical perturbation theory., Comment: 26 pages, 6 figures

We revisit a textbook example of a singularly perturbed nonlinear boundary-value problem. Unexpectedly, it shows a wealth of phenomena that seem to have been overlooked previously, including a pitchfork bifurcation in the number of solutions as one varies the small parameter, and transcendentally small terms in the initial conditions that can be calculated by elementary means. Based on our own classroom experience, we believe this problem could provide an enjoyable workout for students in courses on perturbation methods, applied dynamical systems, or numerical analysis., Comment: 23+2 pages, 8 figures. Supplementary material available at https://github.com/duetosymmetry/surprises-in-a-classic-BVP . Version 2: Added 12 references and additional discussion. Comments welcome