Strong Field Scattering of Black Holes: Assessing Resummation Strategies

TL;DR

This paper evaluates various resummation strategies for high-energy black hole scattering using numerical relativity data, highlighting their limitations and proposing improvements to enhance analytical waveform models for gravitational wave predictions.

Contribution

It introduces new high-energy black hole scattering simulations and compares three resummation schemes, analyzing their performance and suggesting ways to improve model accuracy with higher-order information.

Findings

All models show pathological behavior at high energies.

Including higher-order information improves model accuracy.

Further resummation of EOB potentials can enhance agreement.

Abstract

Recent developments in post-Minkowksian (PM) calculations have led to a fast-growing body of weak-field perturbative information. As such, there is major interest within the gravitational wave community as to how this information can be used to improve the accuracy of theoretical waveform models. In this work, we build on recent efforts to validate high-order PM calculations using numerical relativity simulations. We present a new set of high-energy scattering simulations for equal-mass, non-spinning binary black holes, further expanding the existing suite of NR simulations. We outline the basic features of three recently proposed resummation schemes (the $\mathscr{L}$-resummed model, the $w^\mathrm{eob}$ model and the SEOB-PM model) and compare the analytical predictions to our NR data. Each model is shown to demonstrate pathological behaviour at high energies, with common features such as PM hierarchical shifts and divergences. The NR data can also be used to calibrate pseudo-5PM corrections to the scattering angle or EOB radial potentials. In each case, we argue that including higher-order information improves the agreement between the analytical models and NR, though the extent of improvement depends on how this information is incorporated and the choice of analytical baseline. Finally, we demonstrate that further resummation of the EOB radial potentials could be an effective strategy to improving the model agreement.