The first law of binary black hole scattering

TL;DR

This paper extends the first law of binary black hole mechanics to scattering orbits, incorporating dissipative effects and linking scattering and bound orbit descriptions, with implications for gravitational waveform modeling.

Contribution

It introduces a generalized first law for scattering orbits using classical S-matrix and Hamiltonian methods, including dissipative effects for the first time.

Findings

Derived a first law for scattering orbits

Established a boundary-to-bound map linking scattering and bound states

Connected scattering observables to gravitational waveform invariants

Abstract

In the last decade, the first law of binary black hole mechanics played an important unifying role in the gravitational two-body problem. More recently, binary black hole scattering and the application of high-energy physics methods have provided a new avenue into this classical problem. In this Letter, we connect these two themes by extending the first law to the case of scattering orbits. We present derivations based on classical S-matrix, Hamiltonian, and pseudo-Hamiltonian methods, the last of which allows us to include dissipative effects for the first time. Finally, a "boundary to bound" map links this first law to the traditional bound-orbit version. Through this map a little-known observable for scatter orbits, the elapsed proper time, is mapped to the Detweiler redshift for bound orbits, which is an invariant building block in gravitational waveform models.