Seminarium Teorii Względności i Grawitacji

Given an initial data set for the vacuum Einstein equations, KIDs (Killing Initial Data) are additional tensor fields and differential equations on them (restricted to the initial data surface) which, if they exist, are in bijection with Killing vectors on the bulk spacetime. We generalize this well-known construction also to CKIDs (Conformal Killing Initial Data) and cCYKIDs (closed Conformal Killing-Yano Initial Data). Our approach involves an exhaustive search through covariant "propagation identities" up to a given differential order. Important examples of vacuum spacetimes admitting conformal Killing vectors are pp-waves, while those admitting closed conformal Killing-Yano 2-forms are Kerr-NUT-(A)dS spacetimes.This is joint work with Alfonso García-Parrado. [arXiv:1912.04752]