Speaker : B. Whiting

Title : Gauge invariant perturbations of Petrov type D spacetimes

Abstract : The Regge-Wheeler and Zerilli equations are satisfied by gauge invariant perturbations of the Schwarzschild black hole geometry. Both the perturbation of the imaginary part of Ψ2 (a component of the Weyl curvature), and its time derivative, are gauge invariant and solve the Regge-Wheeler equation with different sources. In Type D spacetimes, the Ψ0 and Ψ4 perturbations of the Weyl curvature are also gauge invariant. A number of other gauge invariants have also been previously identified. We wish to explore the framework in which these results hold for Schwarzschild, with the view to determining what generalizations may extend to the Kerr geometry, and presumably to Petrov type D space-times in general. We begin by writing known invariants in a way which would be extendable to Kerr, principally be reinserting all angular and time derivatives, specifically removing the dependence on spin-weighted spherical harmonics (which do not apply for Kerr) in a mode decomposition.