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Black holes offer a unique laboratory for fundamental physics and are crucial for understanding theories beyond Einstein’s theory of general relativity. In this paper, we focus on 4D effective field theories and string-theory inspired models that include scalar fields. We focus on one such model, axi-dilaton gravity, a quadratic gravity theory with two kinetically coupled scalar fields, an axion and a dilaton. To study the evolution and structure of these fields around black holes, we introduce canuda–axidil, the first open-source, parametrized numerical relativity code for quadratic and biscalar gravity. Using this code, we perform single black hole simulations to show the dynamical formation of axion and dilaton hairs and quantify the effect of higher-order terms in coupling and spin. Through these simulations, we measure the impact of black hole spin and curvature coupling strength on the profiles of the axion and dilaton and show that including kinetic coupling between the fields increases the observed deviations from general relativity. Furthermore, we simulate the axion and dilaton fields around a binary black hole coalescence demonstrating the growth of axion hair during the inspiral and the production of radiative modes for both fields. 

As gravitational wave detectors improve in sensitivity, signal-to-noise ratios of compact binary coalescences will dramatically increase, reaching values in the hundreds and potentially thousands. Such strong signals offer both exciting scientific opportunities and pose formidable challenges to the template waveforms used for interpretation. Current waveform models are informed by calibrating or fitting to numerical relativity waveforms and such strong signals may unveil computational errors in generating these waveforms. In this paper, we isolate a single source of computational error, that of the finite grid resolution, and investigate its impact on parameter estimation for aLIGO and Cosmic Explorer. We demonstrate that increasing the inclination angle or decreasing the mass ratio q (q≤1) raises the resolution required for unbiased parameter estimation. We quantify the error associated with the highest-resolution waveform utilized in our study using an extrapolation procedure on the median of recovered posteriors and confirm the accuracy of current waveforms for the synthetic sources. We introduce a measure to predict the necessary numerical resolution for unbiased parameter estimation and use it to predict that current waveforms are suitable for equal and moderately unequal mass binaries for both detectors. However, current waveforms fail to meet accuracy requirements for high signal-to-noise ratio signals from highly unequal mass ratio binaries (q≲1/6), for all inclinations in Cosmic Explorer, and for high inclinations in future updates to LIGO. Given that the resolution requirement becomes more stringent with more unequal mass ratios, current waveforms may lack the necessary accuracy, even at median signal-to-noise ratios for future detectors. 

Abstract 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 early inspirals of stellar-mass black holes that will ultimately 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.