All local gauge invariants for perturbations of the Kerr spacetime

TL;DR

This paper introduces two complex scalar gauge invariants for Kerr spacetime perturbations, constructed covariantly using background symmetries, which, combined with existing invariants, form a minimal generating set for all local gauge invariants.

Contribution

It provides a new covariant construction of gauge invariants for Kerr perturbations, expanding the toolkit for analyzing gravitational perturbations.

Findings

The invariants are sensitive to Kerr parameter variations.

They form a minimal set with Teukolsky scalars and linearized Ricci tensor.

Curvature invariants reduce to gauge invariants in linearized theory.

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.