A proof of conservation laws in gravitational scattering: tails and breaking of peeling

TL;DR

This paper defines a class of asymptotically flat spacetimes compatible with gravitational scattering and proves antipodal matching conditions and conservation laws at spatial infinity.

Contribution

It introduces a consistent framework for asymptotically flat spacetimes and establishes new antipodal matching conditions and conservation laws at spatial infinity.

Findings

Proves antipodal matching conditions for dual mass aspect and shear tail.

Reformulates identities as asymptotic conservation laws on the boundary hyperboloid.

Connects peeling properties at infinities to spatial infinity features.

Abstract

We propose a definition of asymptotically flat spacetimes that is consistent with both null infinities and compatible with known properties of gravitational scattering, incoming and outgoing radiation, and interactions with matter. For this class of spacetimes, we prove three antipodal matching conditions at spatial infinity: one for the so-called dual mass aspect, one for the leading tail of the shear, and one that non-trivially relates the peeling properties of the spacetime at past and null infinities to the leading tail and mass aspect at spatial infinity. Furthermore, we reformulate these identities as asymptotic conservation laws defined on the boundary hyperboloid at spatial infinity.