Comments on the instability of black-hole inner horizons

Abstract

The inner (Cauchy) horizons of Kerr and Reissner-Nordstrom black-hole solutions are unstable against generic, linearized perturbations. Understanding the precise nature of these instabilities is clearly important for cosmic censorship, and a number of recent studies have addressed this issue. In particular, some of the recent papers have challenged the widely accepted view that the instabilities would, in the generic case, turn the Cauchy horizon into a spacelike curvature singularity. Instead, the new results appear to support an alternative picture of the generic black-hole interior in which the perturbed Cauchy horizon is replaced by a null singularity, and one with weaker strength (tidal forces) than was previously believed. To prove these recent conclusions rigorously would require the difficult analysis of the full non-linear perturbation equations in an interior black-hole background. A similar but somewhat simpler model problem to study is perturbations of the Cauchy horizon of a plane-symmetric spacetime; this model, as the authors comment on is not only more tractable, but also provides some interesting formal pointers to the original black-hole inner-horizon problem. They make a number of comments, based entirely on previous work on the dynamics of plane-symmetric spacetimes, that exploit the analogy between these two problems. A straightforward exploration of this analogy appears to support the older picture where a spacelike curvature singularity. rather than a weaker, null one, replaces the inner horizon of a black hole under generic nonlinear perturbations. Their arguments are not conclusive, but they might yield further more rigorous insights when combined with the new techniques other authors use in their analyses.