Precision theory is only useful for gravitational-wave astronomy if it can be translated into waveform models fast enough to use in data analysis. For LISA’s EMRI science case, millions of waveform evaluations are required for a single Bayesian parameter estimation run, each covering months of detector time. For ground-based detectors, the requirements are different but no less demanding.
Our fast-waveforms programme bridges the gap between the expensive field-theory calculations at the heart of self-force theory and the rapid waveform generation required in practice.
A two-stage approach
Our strategy separates the problem into two stages. In the offline stage, we solve the field equations and compute self-force quantities and gravitational-wave fluxes across a grid of orbital configurations. This is computationally expensive but needs to be done only once. In the online stage, we interpolate these pre-computed results and integrate the orbital dynamics to generate a waveform — a process that takes milliseconds on modern hardware. This separation makes real-time Bayesian inference feasible: the expensive physics is pre-computed once, and the online stage is fast enough to be embedded directly in a sampler.
Numerical infrastructure
Fast and accurate waveform generation depends on high-quality numerical solvers for the Teukolsky and related field equations. Our numerical solvers programme develops the frequency-domain and time-domain codes that produce the raw self-force data on which waveform models are built, optimised for both accuracy and performance.
Connecting to other frameworks
Self-force waveforms are not developed in isolation. Our hybrid models programme connects gravitational self-force results to effective-one-body and post-Newtonian frameworks, extending the reach of self-force-based models into higher mass-ratio regimes where both approaches are applicable and cross-validating results across methods.
Applications
The waveforms we develop are directly relevant to LISA data analysis pipelines for the detection and characterisation of EMRIs, to ground-based detector searches for intermediate mass-ratio systems with LIGO-Virgo-KAGRA and next-generation observatories such as the Einstein Telescope and Cosmic Explorer, and to precision tests of general relativity in the strong-field regime.