Gravitational instabilities in Kerr spacetimes

IGNACIO FRANCISCO RANEA SANDOVAL

La Falda

Congreso; Grav09; 2009

FaMAF-UNC

In this talk we consider the possible existence of unstable axisymmetric modes in Kerr space times. We describe a transformation that casts Teukolsky's radial equation in the form of a unidimensional Schrödinger equation, and combine the properties of the solutions of this equations with some recent results on the asymptotic behaviour of spin weighted spheroidal harmonics to prove the existence of an infinite family of unstable modes. Thus we prove that the stationary region beyond a Kerr black hole inner horizon is unstable under gravitational linear perturbations. We also prove that Kerr space-time with angular momentum larger than its square mass, which has a naked singularity, is unstable.