When two black holes spiral together and collide, they send ripples through spacetime that future gravitational-wave detectors will measure with far greater precision than today’s instruments can manage. But those detectors will only be as good as the theoretical models that predict what the waves should look like—and current models are not accurate enough to avoid introducing systematic errors in the interpretation of the data. This project tackles that gap by studying black holes that fly past each other in hyperbolic, unbound orbits rather than circling inward. A recently discovered mathematical mapping connects these scattering encounters to the bound inspiral that actually produces detectable gravitational waves. The researchers will use self-force theory—a method from general relativity that works precisely for systems with very unequal masses—to calculate scattering observables through second order in the mass ratio. This will extend the validity of existing waveform models into the strong-field regime where black holes interact most violently. The work is fundamental science. It will not change anyone’s daily life directly. But if successful, it will eliminate a key source of modelling bias in gravitational-wave astronomy, allowing future observatories to extract cleaner information about black hole populations, the expansion history of the universe, and the behaviour of gravity under extreme conditions—much as earlier fundamental work on numerical relativity made the first LIGO detections possible.
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The inspiral and merger of binary black hole (BBH) systems will continue to be prime target for gravitational-wave searches as we approach the era of third-generation and space-based observatories. The sensitivity increase and access to lower-frequency bands will allow us to see much further into cosmological history, probe BBH mergers with exquisite precision, and bring to view new types of merger phenomena. As detector sensitivity improves, so too must the accuracy of our waveform models, to minimise systematic biases in parameter recovery due simply to modelling error. And as detectors become sensitive to sources with a broader range of physical properties (mass disparity, eccentricity, spin configurations), our models must be extended to capture the new physics. Within this effort, a fascinating new technique has recently emerged, based on the study of BBHs in hyperbolic scattering. While scattering scenarios are not themeselves important sources of observable gravitational waves, they can provide a remarkably efficient handle on the general-relativistic dynamics in astrophysically relevant, bound BBHs. This is thanks to a remarkable "unbound to bound" mapping that has been discovered recently between certain orbital observables---e.g., one relating scattering angle to periastron advance. This mapping underpins the relevance of recent endeavours to apply QCD-inspired scattering-amplitude methods to the BBH problem. While remarkably successful, such calculations are primarily post-Minkowskian (PM), a-priori restricted to weak interaction. This we began to remedy in recent work by applying methods from self-force theory, with scattering observables now calculated in full General Relativity, albeit expanded in the BBH's mass ratio. Our exploratory work has already led to interesting synergies with Amplitudes calculations, and demonstrates how the validity of the latter can be extended to the strong-field regime through hybridisation with self-force results. Our aim here is to consolidate these initial explorations into a coherent programme to improve BBH waveform models using self-force calculations in scattering orbits. It has 3 interweaving strands. (1) Extend current toy-model analysis to the full BBH problem (without spin), calculating scattering observables through second order in the mass ratio. (This, as a by-product, will give a complete description of the radiative dynamics at any mass ratio through 6PM order, well beyond current knowledge.) (2) Formulate unbound-to-bound mapping in the context of self-force theory, and thus apply our results to bound BBHs. (3) Use our results within existing BBH modelling frameworks---self-force, Effective One Body, Numerical Relativity---to improve the accuracy, speed, and parameter-space reach of current waveform generators.
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