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

Abstract

Reissner--Nordström 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.

24 pages, 4 figures. Changes and corrections in proof using intertwiners, also in figures

References in corpus (6)

• Classical instability of Kerr-AdS black holes and the issue of final state
• Instability of hyper-compact Kerr-like objects
• Instability of charged and rotating naked singularities
• Gravitational instabilities in Kerr space-times
• Stability of naked singularities and algebraically special modes
• Instabilities of naked singularities and black hole interiors in General Relativity

Cited by in corpus (12)

• Motion of charged test particles in Reissner--Nordström spacetime
• Distinguishing Brans-Dicke-Kerr type naked singularities and black holes with their thin disk electromagnetic radiation properties
• Unstable fields in Kerr spacetimes
• Rescuing Complementarity With Little Drama
• The wave equation on the extreme Reissner-Nordström black hole
• Magnetised accretion discs in Kerr spacetimes
• Black hole nonmodal linear stability: odd perturbations of Reissner-Nordström
• Linear Stability of Black Holes and Naked Singularities
• Quasinormal Modes and Stability of Firewalls
• Instabilities in Kerr Spacetimes
• Axisymmetric Solutions to Einstein Field Equations via Integral Transforms
• Perturbations of Einstein--Maxwell--phantom spacetime: Instabilities of charged Ellis--Bronnikov wormholes and quasinormal modes of black holes