All Local Gauge Invariants for Perturbations of the Kerr Spacetime
Journal article, 2018
We present two complex scalar gauge invariants for perturbations of the Kerr spacetime defined covariantly in terms of the Killing vectors and the conformal Killing-Yano tensor of the background together with the linearized curvature and its first derivatives. These invariants are, in particular, sensitive to variations of the Kerr parameters. Together with the Teukolsky scalars and the linearized Ricci tensor, they form a minimal set that generates all local gauge invariants. We also present curvature invariants that reduce to the gauge invariants in the linearized theory.