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Perturbation theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive perturbation theory often fails on long timescales, leading to secularly growing solutions. These divergences have been treated with a variety of techniques, including the powerful dynamical renormalization group (DRG). Most of the existing DRG approaches rely on having analytic solutions up to some order in perturbation theory. However, sometimes the equations can only be solved numerically. We reformulate the DRG in the language of differential geometry, which allows us to apply it to numerical solutions of the background and perturbation equations. This formulation also enables us to use the DRG in systems with background parameter flows, and therefore, extend our results to any order in perturbation theory. As an example, we apply this method to calculate the soliton-like solutions of the Korteweg-de Vries equation deformed by adding a small damping term. We numerically construct DRG solutions which are valid on secular time scales, long after naive perturbation theory has broken down., Comment: 22+5 pages, 20 figures, 3 tables. References added. Matches the version published in PRE. Comments are welcome

Understanding the Bondi-Metzner-Sachs (BMS) frame of the gravitational waves produced by numerical relativity is crucial for ensuring that analyses on such waveforms are performed properly. It is also important that models are built from waveforms in the same BMS frame. Up until now, however, the BMS frame of numerical waveforms has not been thoroughly examined, largely because the necessary tools have not existed. In this paper, we show how to analyze and map to a suitable BMS frame for numerical waveforms calculated with the Spectral Einstein Code (SpEC). However, the methods and tools that we present are general and can be applied to any numerical waveforms. We present an extensive study of 13 binary black hole systems that broadly span parameter space. From these simulations, we extract the strain and also the Weyl scalars using both SpECTRE's Cauchy-characteristic extraction module and also the standard extrapolation procedure with a displacement memory correction applied during postprocessing. First, we show that the current center-of-mass correction used to map these waveforms to the center-of-mass frame is not as effective as previously thought. Consequently, we also develop an improved correction that utilizes asymptotic Poincar\'e charges instead of a Newtonian center-of-mass trajectory. Next, we map our waveforms to the post-Newtonian (PN) BMS frame using a PN strain waveform. This helps us find the unique BMS transformation that minimizes the $L^{2}$ norm of the difference between the numerical and PN strain waveforms during the early inspiral phase. We find that once the waveforms are mapped to the PN BMS frame, they can be hybridized with a PN strain waveform much more effectively than if one used any of the previous alignment schemes, which only utilize the Poincar\'e transformations., Comment: 18 pages, 11 figures; Published in Physical Review D

We present a new study of remnant black hole properties from 13 binary black hole systems, numerically evolved using the Spectral Einstein Code. The mass, spin, and recoil velocity of each remnant were determined quasi-locally from apparent horizon data and asymptotically from Bondi data $(h, \psi_4, \psi_3, \psi_2, \psi_1)$ computed at future null infinity using SpECTRE's Cauchy characteristic evolution. We compare these independent measurements of the remnant properties in the bulk and on the boundary of the spacetime, giving insight into how well asymptotic data are able to reproduce local properties of the remnant black hole in numerical relativity. We also discuss the theoretical framework for connecting horizon quantities to asymptotic quantities and how it relates to our results. This study recommends a simple improvement to the recoil velocities reported in the Simulating eXtreme Spacetimes waveform catalog, provides an improvement to future surrogate remnant models, and offers new analysis techniques for evaluating the physical accuracy of numerical simulations., Comment: 14 pages, 4 figures, 1 table; published Physical Review D

Self consistent solution to electromagnetic (EM)-circuit systems is of significant interest for a number of applications. This has resulted in exhaustive research on means to couple them. In time domain, this typically involves a tight integration (or coupling) with field and non-linear circuit solvers. This is in stark contrast to coupled analysis of linear/weakly non-linear circuits and EM systems in frequency domain. Here, one typically extracts equivalent port parameters that are then fed into the circuit solver. Such an approach has several advantages; (a) the number of ports is typically smaller than the number of degrees of freedom, resulting in cost savings; (b) is circuit agnostic; (c) can be integrated with a variety of device models. Port extraction is tantamount to obtaining impulse response of the linear EM system. In time domain, the deconvolution required to effect this is unstable. Recently, a novel approach was developed for time domain integral equations to overcome this bottleneck. We extend this approach to time domain finite element method, and demonstrate its utility via a number of examples; significantly, we demonstrate that self consistent solutions obtained using either a fully coupled or port extraction is identical to the desired precision for non-linear circuit systems. This is shown within a nodal network. We also demonstrate integration of port extracted data directly with drift diffusion equation to model device physics., Comment: 9 pages, 7 figures

We perform a new test of general relativity (GR) with signals from GWTC-2, the LIGO and Virgo catalog of gravitational wave detections. We search for the presence of amplitude birefringence, in which left versus right circularly polarized modes of gravitational waves are exponentially enhanced and suppressed during propagation. Such an effect is present in various beyond-GR theories but is absent in GR. We constrain the amount of amplitude birefringence consistent with the data through an opacity parameter $\kappa$, which we bound to be $\kappa \lesssim 0.74 \textrm{ Gpc}^{-1}$. We then use these theory-agnostic results to constrain Chern-Simons gravity, a beyond-GR theory with motivations in quantum gravity. We bound the canonical Chern-Simons lengthscale to be $\ell_0 \lesssim 1.0 \times 10^3$ km, improving on previous long-distance measurement results by a factor of two., Comment: Updated to match published version, 8 pages (+6 pages of appendices), 7 figures

Accurate and efficient modeling of the dynamics of binary black holes (BBHs) is crucial to their detection and parameter estimation through gravitational waves, both with LIGO/Virgo and LISA. General BBH configurations will have misaligned spins and eccentric orbits, eccentricity being particularly relevant at early times. Modeling these systems is both analytically and numerically challenging. Even though the 1.5 post-Newtonian (PN) order is Liouville integrable, numerical work has demonstrated chaos at 2PN order, which impedes the existence of an analytic solution. In this article we revisit integrability at both 1.5PN and 2PN orders. At 1.5PN, we construct four (out of five) action integrals. At 2PN, we show that the system is indeed integrable - but in a perturbative sense - by explicitly constructing five mutually-commuting constants of motion. Because of the KAM theorem, this is consistent with the past numerical demonstration of chaos. Our method extends to higher PN orders, opening the door for a fully analytical solution to the generic eccentric, spinning BBH problem., Comment: 11+2 pages, 2 figures, 1 ancillary Mathematica file; v2: Updated to match version accepted by PRD

Gravitational-wave memory effects are identified by their distinctive effects on families of freely falling observers: after a burst of waves pass by their locations, memory effects can cause lasting relative displacements of the observers. These effects are closely related to the infrared properties of gravity and other massless field theories, including their asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in Brans-Dicke theory. We compute the field equations in Bondi coordinates, and we define a set of boundary conditions that represent asymptotically flat solutions in this context. Next, we derive the asymptotic symmetry group of these spacetimes, and we find that it is the same as the Bondi-Metzner-Sachs group in general relativity. Because there is an additional polarization of gravitational waves in Brans-Dicke theory, we compute the memory effects associated with this extra polarization (the so-called "breathing" mode). This breathing mode produces a uniform expansion (or contraction) of a ring of freely falling observers. After these breathing gravitational waves pass by the observers' locations, there are two additional memory effects that depend on their initial displacements and relative velocities. Neither of these additional memory effects seems to be related to asymptotic symmetries or conserved quantities; rather, they are determined by the properties of the nonradiative region before and after the bursts of the scalar field and the gravitational waves. We discuss the properties of these regions necessary to support nontrivial breathing-mode-type memory effects., Comment: Appendix added, section 2B modified, minor modifications to the introduction, matches published version

Understanding distributions of black holes is crucial to both astrophysics and quantum gravity. Studying astrophysical population statistics has even been suggested as a channel to constrain black hole formation from the quantum vacuum. Here we propose a Gedankenexperiment to show that the non-linear properties of binary mergers (simulated with accurate surrogate models) generate an attractor in the space of distributions. Our results show that the joint distribution of spin magnitude and fractional mass loss evolves to a fixed point, converging in a few generations. The features of this fixed point distribution do not depend on the choice of initial distribution. Since a black hole merger is irreversible it produces entropy - possibly the largest source of entropy in the universe. The fixed-point distributions are neither isothermal nor isentropic, and initially thermodynamic states evolve away from thermality. We finally evaluate the specific entropy production rate per merger from initially thermal and non-thermal distributions, which converges to a constant., Comment: Major revision and results updated. New appendix included. Tested convergence of the joint 2D-3D PDFs and independence of the kick velocity. 9+2 pages. 12 Figures. Comments are welcome

Black hole spacetimes, like the Kerr spacetime, admit both stable and plunging orbits, separated in parameter space by the separatrix. Determining the location of the separatrix is of fundamental interest in understanding black holes, and is of crucial importance for modeling extreme mass-ratio inspirals. Previous numerical approaches to locating the Kerr separatrix were not always efficient or stable across all of parameter space. In this paper we show that the Kerr separatrix is the zero set of a single polynomial in parameter space. This gives two main results. First, we thoroughly analyze special cases (extreme Kerr, polar orbits, etc.), finding strict bounds on the limits of roots, and unifying a number of results in the literature. Second, we pose a stable numerical method which is guaranteed to quickly and robustly converge to the separatrix. This new approach is implemented in the Black Hole Perturbation Toolkit, and results in a ~45x speedup over the prior robust approach., Comment: 11+4 pages, 6 figures, 1 ancillary Mathematica file. v2: Minor edits, matched version published in PRD. Code available at https://bhptoolkit.org/

We produce the first astrophysically-relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first LIGO detection, in order-reduced dynamical Chern-Simons gravity, a theory with motivations in string theory and loop quantum gravity. We present results for the leading-order corrections to the merger and ringdown waveforms, as well as the ringdown quasi-normal mode spectrum. We estimate that such corrections may be discriminated in detections with signal to noise ratio $\gtrsim 180-240$, with the precise value depending on the dimension of the GR waveform family used in data analysis., Comment: 7 pages + appendices, 8 figures, Updated to match Phys. D. Rev article

$\mathtt{qnm}$ is an open-source Python package for computing the Kerr quasinormal mode frequencies, angular separation constants, and spherical-spheroidal mixing coefficients. The $\mathtt{qnm}$ package includes a Leaver solver with the Cook-Zalutskiy spectral approach to the angular sector, and a caching mechanism to avoid repeating calculations. We provide a large cache of low $\ell, m, n$ modes, which can be downloaded and installed with a single function call, and interpolated to provide good initial guess for root-polishing at new values of spin., Comment: 3 pages, 0 figures. Matches version accepted by the Journal of Open Source Software. The source repository: https://github.com/duetosymmetry/qnm , PyPI entry: https://pypi.org/project/qnm/ , documentation: https://qnm.readthedocs.io . Suggestions and pull requests welcome

Magnetic resonance imaging (MRI) has great potential to improve prostate cancer diagnosis. It can spare men with a normal exam from undergoing invasive biopsy while making biopsies more accurate in men with lesions suspicious for cancer. Yet, the subtle differences between cancer and confounding conditions, render the interpretation of MRI challenging. The tissue collected from patients that undergo pre-surgical MRI and radical prostatectomy provides a unique opportunity to correlate histopathology images of the entire prostate with MRI in order to accurately map the extent of prostate cancer onto MRI. Here, we introduce the RAPSODI (framework for the registration of radiology and pathology images. RAPSODI relies on a three-step procedure that first reconstructs in 3D the resected tissue using the serial whole-mount histopathology slices, then registers corresponding histopathology and MRI slices, and finally maps the cancer outlines from the histopathology slices onto MRI. We tested RAPSODI in a phantom study where we simulated various conditions, e.g., tissue specimen rotation upon mounting on glass slides, tissue shrinkage during fixation, or imperfect slice-to-slice correspondences between histology and MRI. Our experiments showed that RAPSODI can reliably correct for rotations within $\pm15^{\circ}$ and shrinkage up to 10%. We also evaluated RAPSODI in 89 patients from two institutions that underwent radical prostatectomy, yielding 543 histopathology slices that were registered to corresponding T2 weighted MRI slices. We found a Dice coefficient of 0.98$ \pm $0.01 for the prostate, prostate boundary Hausdorff distance of 1.71$ \pm $0.48 mm, a urethra deviation of 2.91$ \pm $1.25 mm, and a landmark deviation of 2.88$ \pm $0.70 mm between registered histopathology images and MRI. Our robust framework successfully mapped the extent of disease from histopathology slices onto MRI., Comment: version 2

We produce the first numerical relativity binary black hole gravitational waveforms in a higher-curvature theory beyond general relativity. In particular, we study head-on collisions of binary black holes in order-reduced dynamical Chern-Simons gravity. This is a precursor to producing beyond-general-relativity waveforms for inspiraling binary black hole systems that are useful for gravitational wave detection. Head-on collisions are interesting in their own right, however, as they cleanly probe the quasi-normal mode spectrum of the final black hole. We thus compute the leading-order dynamical Chern-Simons modifications to the complex frequencies of the post-merger gravitational radiation. We consider equal-mass systems, with equal spins oriented along the axis of collision, resulting in remnant black holes with spin. We find modifications to the complex frequencies of the quasi-normal mode spectrum that behave as a power law with the spin of the remnant, and that are not degenerate with the frequencies associated with a Kerr black hole of any mass and spin. We discuss these results in the context of testing general relativity with gravitational wave observations., Comment: 13 pages (+ appendices), 15 figures

Only numerical relativity simulations can capture the full complexities of binary black hole mergers. These simulations, however, are prohibitively expensive for direct data analysis applications such as parameter estimation. We present two new fast and accurate surrogate models for the outputs of these simulations: the first model, NRSur7dq4, predicts the gravitational waveform and the second model, \RemnantModel, predicts the properties of the remnant black hole. These models extend previous 7-dimensional, non-eccentric precessing models to higher mass ratios, and have been trained against 1528 simulations with mass ratios $q\leq4$ and spin magnitudes $\chi_1,\chi_2 \leq 0.8$, with generic spin directions. The waveform model, NRSur7dq4, which begins about 20 orbits before merger, includes all $\ell \leq 4$ spin-weighted spherical harmonic modes, as well as the precession frame dynamics and spin evolution of the black holes. The final black hole model, \RemnantModel, models the mass, spin, and recoil kick velocity of the remnant black hole. In their training parameter range, both models are shown to be more accurate than existing models by at least an order of magnitude, with errors comparable to the estimated errors in the numerical relativity simulations. We also show that the surrogate models work well even when extrapolated outside their training parameter space range, up to mass ratios $q=6$., Comment: Matches published version. Models publicly available at https://zenodo.org/record/3455886#.XZ9s1-dKjBI and https://pypi.org/project/surfinBH

Accurate models of gravitational waves from merging black holes are necessary for detectors to observe as many events as possible while extracting the maximum science. Near the time of merger, the gravitational waves from merging black holes can be computed only using numerical relativity. In this paper, we present a major update of the Simulating eXtreme Spacetimes (SXS) Collaboration catalog of numerical simulations for merging black holes. The catalog contains 2018 distinct configurations (a factor of 11 increase compared to the 2013 SXS catalog), including 1426 spin-precessing configurations, with mass ratios between 1 and 10, and spin magnitudes up to 0.998. The median length of a waveform in the catalog is 39 cycles of the dominant $\ell=m=2$ gravitational-wave mode, with the shortest waveform containing 7.0 cycles and the longest 351.3 cycles. We discuss improvements such as correcting for moving centers of mass and extended coverage of the parameter space. We also present a thorough analysis of numerical errors, finding typical truncation errors corresponding to a waveform mismatch of $\sim 10^{-4}$. The simulations provide remnant masses and spins with uncertainties of 0.03% and 0.1% ($90^{\text{th}}$ percentile), about an order of magnitude better than analytical models for remnant properties. The full catalog is publicly available at https://www.black-holes.org/waveforms ., Comment: 33+18 pages, 13 figures, 4 tables, 2,018 binaries. Catalog metadata in ancillary JSON file. v2: Matches version accepted by CQG. Catalog available at https://www.black-holes.org/waveforms

Binary black hole mergers are of great interest to the astrophysics community, not least because of their promise to test general relativity in the highly dynamic, strong field regime. Detections of gravitational waves from these sources by LIGO and Virgo have garnered widespread media and public attention. Among these sources, precessing systems (with misaligned black-hole spin/orbital angular momentum) are of particular interest because of the rich dynamics they offer. However, these systems are, in turn, more complex compared to nonprecessing systems, making them harder to model or develop intuition about. Visualizations of numerical simulations of precessing systems provide a means to understand and gain insights about these systems. However, since these simulations are very expensive, they can only be performed at a small number of points in parameter space. We present binaryBHexp, a tool that makes use of surrogate models of numerical simulations to generate on-the-fly interactive visualizations of precessing binary black holes. These visualizations can be generated in a few seconds, and at any point in the 7-dimensional parameter space of the underlying surrogate models. With illustrative examples, we demonstrate how this tool can be used to learn about precessing binary black hole systems., Comment: Matches CQG version. Visualizations available at https://vijayvarma392.github.io/binaryBHexp