Gravitational instabilities in Kerr space-times

Details Gravitational instabilities in Kerr space-times Gravitational instabilities in Kerr space-times

2008-05-28

arxiv.org/abs/0805.4306v3

Class.Quant.Grav.25:245012,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, 4 figures, comments, references and calculation details added, asymptotic expansion typos fixed

Scientific paper

10.1088/0264-9381/25/24/245012

In this paper we consider the possible existence of unstable axisymmetric modes in Kerr space times, resulting from exponentially growing solutions of the Teukolsky equation. We describe a transformation that casts the radial equation that results upon separation of variables in the Teukolsky equation, in the form of a Schr\"odinger 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.

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