Gravitational instability of the inner static region of a Reissner-Nordstrom black hole

TL;DR

This paper proves that the inner static region of Reissner-Nordstrom black holes is linearly unstable under gravitational perturbations, supporting the strong cosmic censorship conjecture and extending the analysis to naked singularities.

Contribution

It demonstrates the linear instability of the inner static region of Reissner-Nordstrom black holes using intertwiners, and links the Zerilli field to a geometric Riemann tensor invariant.

Findings

Inner static region is unstable under perturbations

Supports strong cosmic censorship conjecture

Instability extends to super-extremal Reissner-Nordstrom black holes

Abstract

Reissner--Nordstr\"om black holes have two static regions: $r > \ro$ and $0 < r < \ri$, where $\ri$ and $\ro$ are the inner and outer horizon radii. The stability of the exterior static region has been established long time ago. In this work we prove that the interior static region is unstable under linear gravitational perturbations, by showing that field perturbations compactly supported within this region will generically excite a mode that grows exponentially in time. This result gives an alternative reason to mass inflation to consider the space time extension beyond the Cauchy horizon as physically irrelevant, and thus provides support to the strong cosmic censorship conjecture, which is also backed by recent evidence of a linear gravitational instability in the interior region of Kerr black holes found by the authors. The use of intertwiners to solve for the evolution of initial data plays a key role, and adapts without change to the case of super-extremal \rn black holes, allowing to complete the proof of the linear instability of this naked singularity. A particular intertwiner is found such that the intertwined Zerilli field has a geometrical meaning -it is the first order variation of a particular Riemann tensor invariant-. Using this, calculations can be carried out explicitely for every harmonic number.