Petrov type of linearly perturbed type-D spacetimes

BERNARDO ARANEDA; GUSTAVO DOTTI

CLASSICAL AND QUANTUM GRAVITY

IOP PUBLISHING LTD

Lugar: Londres; Año: 2015 vol. 32 p. 1 - 13

0264-9381

We show that a spacetime satisfying the linearized vacuum Einstein equationsaround a type-D background is generically of type I, and that the splittings ofthe principal null directions (PNDs) and of the degenerate eigenvalue of theWeyl tensor are non-analytic functions of the perturbation parameter of themetric. This provides a gauge-invariant characterization of the effect of theperturbation on the underlying geometry, without appealing to differentialcurvature invariants. This is of particular interest for the Schwarzschildsolution, for which there are no signatures of the even perturbations on thealgebraic curvature invariants. We also show that, unlike the general case, theunstable even modes of the Schwarzschild naked singularity deform the Weyltensor into a type-II one.