Instabilities of naked singularities and black hole interiors in General Relativity

TL;DR

This paper reviews recent findings that naked singularities and certain black hole interior regions in General Relativity are linearly unstable, supporting the cosmic censorship conjecture and enhancing understanding of black hole stability.

Contribution

It demonstrates the linear instability of naked singularities and the inner regions of Kerr black holes, providing evidence for cosmic censorship in General Relativity.

Findings

Naked singularities are linearly unstable under gravitational perturbations.

Inner regions beyond the Kerr black hole's inner horizon are also unstable.

Results support the cosmic censorship conjecture.

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-N\"ordstrom 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.