Black hole scattering with numerical methods and the resummation of weak-field analytic expressions

Recent advances in modelling unbound binary black hole interactions have been driven by the application of scattering amplitude methods from high-energy physics to generate results within the post-Minkowskian (PM) expansion. However, this expansion breaks down when approaching the strong-field regime, where large curvature effects become non-negligible. In this talk, I will present recent progress in the numerical modelling of strong-field black hole scattering using two complementary approaches.

First, I will demonstrate how compactified hyperboloidal coordinates enable stable evolution of the Teukolsky equation in the self-force (SF) framework. Second, I will show how strong-field SF information can be used to resum the weak-field PM and post-Newtonian series, yielding accurate predictions of radiative quantities across all separations for both bound and unbound orbits.

Finally, I will discuss the adaptation of the Spectral Einstein Code (SpEC) to perform highly accurate Numerical Relativity simulations of black hole scattering, which have allowed the extraction of higher-order SF coefficients and the benchmarking of PM expressions.