Gravitational instabilities in Kerr space times

G. DOTTI; R. J. GLEISER; I.F.RANEA-SANDOVAL; H. VUCETICH

CLASSICAL AND QUANTUM GRAVITY

IOP PUBLISHING LTD

Año: 2008 vol. 25 p. 245012 - 245012

0264-9381

In this paper we consider the possible existence of unstable axisymmetricmodes in Kerr spacetimes, resulting from exponentially growing solutions ofthe Teukolsky equation. We describe a transformation that casts the radialequation that results upon separation of variables in the Teukolsky equation, inthe form of a Schr¨odinger equation, and combine the properties of the solutionsof this equations with some recent results on the asymptotic behaviour of spinweighted spheroidal harmonics to prove the existence of an infinite family ofunstable modes. Thus we prove that the stationary region beyond a Kerr blackhole inner horizon is unstable under gravitational linear perturbations. We alsoprove that Kerr spacetime with angular momentum larger than its square mass,which has a naked singularity, is unstable