We present the first numerical relativity waveforms for binary black hole mergers produced using spectral methods that show both the displacement and the spin memory effects. Explicitly, we use the SXS (Simulating eXtreme Spacetimes) Collaboration's SpEC code to run a Cauchy evolution of a binary black hole merger and then extract the gravitational wave strain using SpECTRE's version of a Cauchycharacteristic extraction. We find that we can accurately resolve the strain's traditional m ¼ 0 memory modes and some of the m ≠ 0 oscillatory memory modes that have previously only been theorized. We also perform a separate calculation of the memory using equations for the Bondi-Metzner-Sachs charges as well as the energy and angular momentum fluxes at asymptotic infinity. Our new calculation uses only the gravitational wave strain and two of the Weyl scalars at infinity. Also, this computation shows that the memory modes can be understood as a combination of a memory signal throughout the binary's inspiral and merger phases, and a quasinormal mode signal near the ringdown phase. Additionally, we find that the magnetic memory, up to numerical error, is indeed zero as previously conjectured. Last, we find that signalto-noise ratios of memory for LIGO, the Einstein Telescope, and the Laser Interferometer Space Antenna with these new waveforms and new memory calculation are larger than previous expectations based on post-Newtonian or minimal waveform models.

Accurate models of gravitational waves from merging binary black holes are crucial for detectors to measure events and extract new science. One important feature that is currently missing from the Simulating eXtreme Spacetimes (SXS) Collaboration's catalog of waveforms for merging black holes, and other waveform catalogs, is the gravitational memory effect: a persistent, physical change to spacetime that is induced by the passage of transient radiation. We find, however, that by exploiting the Bondi-Metzner-Sachs (BMS) balance laws, which come from the extended BMS transformations, we can correct the strain waveforms in the SXS catalog to include the missing displacement memory. Our results show that these corrected waveforms satisfy the BMS balance laws to a much higher degree of accuracy. Furthermore, we find that these corrected strain waveforms coincide especially well with the waveforms obtained from Cauchy-characteristic extraction (CCE) that already exhibit memory effects. These corrected strain waveforms also evade the transient junk effects that are currently present in CCE waveforms. Lastly, we make our code for computing these contributions to the BMS balance laws and memory publicly available as a part of the python package sxs, thus enabling anyone to evaluate the expected memory effects and violation of the BMS balance laws.

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-ofmass frame is not as effective as previously thought. Consequently, we also develop an improved correction that utilizes asymptotic Poincaré 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 Poincaré transformations.

Quasinormal mode (QNM) modeling is an invaluable tool for characterizing remnant black holes, studying strong gravity, and testing general relativity. Only recently have QNM studies begun to focus on multimode fitting to numerical relativity strain waveforms. As gravitational wave 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 I þ . 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), a waveform 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 allmode strain mismatch improves by a factor of ∼10 5 when using multimode fitting as opposed to only fitting the ð2; AE2; nÞ 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 waveformswhich exhibit the memory effect-to a BMS frame known as the super rest frame, there is an improvement of ∼10 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 allmode mismatches that are, on average, a factor of ∼4 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 numerical relativity and comparing our results to previous QNM studies.

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 quasilocally from apparent horizon data and asymptotically from Bondi data ðh; ψ 4 ; ψ 3 ; ψ 2 ; ψ 1 Þ 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.