Instabilities of naked singularities and black hole interiors in General Relativity

Abstract

Metrics representing black holes in General Relativity may exhibit naked singularities for certain values of their parameters. This is the case for super-extremal ($J^2>M>0$) Kerr and super-extremal ($|Q|>M>0$) Reissner-Nördstrom spacetimes, and also for the negative mass Schwarzschild spacetime. We review our recent work where we show that these nakedly singular spacetimes are unstable under linear gravitational perturbations, a result that supports the cosmic censorship conjecture, and also that the inner stationary region beyond the inner horizon of a Kerr black hole ($J^2<M$) is linearly unstable.

arXiv commentReview talk given at the 7th Friedmann Seminar, Joao Pessoa, Brazil, July 2008

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• Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions
• On the stability of naked singularities
• Instability of the negative mass Schwarzschild naked singularity
• Instability of charged and rotating naked singularities
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• Unstable fields in Kerr spacetimes
• Naked Singularities, Topological Defects and Brane Couplings
• On the causal characterization of singularities in spherically symmetric spacetimes
• Axial gravitational perturbations of an infinite static line source
• Instabilities in Kerr Spacetimes
• Linear stability of the Linet - Tian solution with negative cosmological constant