Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. II. KIDs for the Kerr-(A)(de Sitter) family

Abstract

We characterize Cauchy data sets leading to vacuum space-times with vanishing Mars-Simon tensor. This approach provides an algorithmic procedure to check whether a given initial data set $(\Sigma,h_{ij},K_{ij})$ evolves into a space-time which is locally isometric to a member of the Kerr-(A)(dS) family.