On Killing vectors in initial value problems for asymptotically flat space-times

TL;DR

This paper investigates conditions for the existence of Killing vectors in asymptotically flat space-times using initial value problem formulations, providing necessary and sufficient criteria in conformally compactified settings.

Contribution

It introduces new implicit conditions for Killing vectors in asymptotic initial value problems on conformally compactified space-times.

Findings

Derived necessary and sufficient conditions for Killing vectors

Applied conditions to characteristic and hyperboloidal initial value problems

Enhanced understanding of symmetries in asymptotically flat space-times

Abstract

The existence of symmetries in asymptotically flat space-times are studied from the point of view of initial value problems. General necessary and sufficient (implicit) conditions are given for the existence of Killing vector fields in the asymptotic characteristic and in the hyperboloidal initial value problem (both of them are formulated on the conformally compactified space-time manifold).