All local gauge invariants for perturbations of the Kerr spacetime

Abstract

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 linearized theory.

arXiv comment5 pages. Updated references

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• A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes
• Compatibility complexes of overdetermined PDEs of finite type, with applications to the Killing equation
• Minimum Resolution of the Minkowski, Schwarzschild and Kerr Differential Modules
• Generating Compatibility Conditions in Mathematical Physics
• Scalar Curvature Invariants in Classical and Quantum Gravity