Resummed energy loss in extreme-mass-ratio scattering using critical orbits

TL;DR

This paper develops a resummation scheme for gravitational wave energy emission in extreme-mass-ratio black hole scattering, bridging weak and strong-field regimes, and validates it with numerical perturbation theory results.

Contribution

It introduces a universal interpolation formula for radiated energy in black hole scattering, incorporating strong-field divergence behavior and validated through numerical calculations.

Findings

Derived universal formulas for energy emitted to infinity and horizon

Validated formulas with numerical black hole perturbation data

Identified divergence structure near the scattering-plunge boundary

Abstract

Motivated by recent efforts to bridge between weak-field and strong-field descriptions of black-hole binary dynamics, we develop a resummation scheme for post-Minkowskian radiative observables in extreme-mass-ratio scattering, augmented with post-Newtonian terms. Specifically, we derive universal interpolation formulas for the total energy emitted in gravitational waves out to infinity and down the event horizon of the large black hole, valid to leading order in the small mass ratio. We test our formulas using numerical results from direct calculations in black hole perturbation theory. The central idea of our approach is to utilize as a strong-field diagnostic the known form of divergence in the radiated energy along geodesics near the parameter-space separatrix between scattering and plunge. The dominant, logarithmic term of this divergence can be expressed in terms of instantaneous energy fluxes calculated along the unstable circular geodesics that form the separatrix, fluxes that we obtain using interpolation of highly accurate numerical data. The same idea could be applied to bound-orbit radiative observables via either unbound-to-bound mapping or a direct resummation of bound-orbit post-Newtonian expressions.