An asymptotic framework for gravitational scattering
Geoffrey Compère, Samuel E. Gralla, Hongji Wei
Abstract
Abstract Asymptotically flat spacetimes have been studied in five separate regions: future/past timelike infinity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:msup><mml:mi>i</mml:mi><mml:mo>±</mml:mo></mml:msup></mml:math> , future/past null infinity , and spatial infinity i 0 . We formulate assumptions and definitions such that the five infinities share a single Bondi–Metzner–Sachs (BMS) group of asymptotic symmetries and associated charges. We show how individual ingoing/outgoing massive bodies may be ascribed initial/final BMS charges and derive global conservation laws stating that the change in total charge is balanced by the corresponding radiative flux. This framework provides a foundation for the study of asymptotically flat spacetimes containing ingoing and outgoing massive bodies, i.e. for generalized gravitational scattering. Among the new implications are rigorous definitions for quantities like initial/final spin, scattering angle, and impact parameter in multi-body spacetimes, without the use of any preferred background structure.