Final State of Gregory-Laflamme Instability

TL;DR

This paper investigates the evolution of a perturbed 5D black string under Gregory-Laflamme instability, revealing a self-similar cascade leading to a fractal horizon and a naked singularity, challenging cosmic censorship.

Contribution

It demonstrates the self-similar, fractal-like evolution of black string horizons during instability, linking gravitational dynamics to fluid instabilities and showing violation of cosmic censorship.

Findings

Horizon evolves as a sequence of black holes connected by unstable string segments.

Self-similar cascade leads to arbitrarily small scales and a naked singularity.

Horizon develops a fractal structure prior to singularity formation.

Abstract

We describe the behavior of a perturbed 5-dimensional black string subject to the Gregory-Laflamme instability. We show that the horizon evolves in a self-similar manner, where at any moment in the late-time development of the instability the horizon can be described as a sequence of 3-dimensional spherical black holes of varying size, joined by black string segments of similar radius. As with the initial black string, each local string segment is itself unstable, and this fuels the self-similar cascade to (classically) arbitrarily small scales; in the process the horizon develops a fractal structure. In finite asymptotic time, the remaining string segments shrink to zero-size, yielding a naked singularity. Since no fine-tuning is required to excite the instability, this constitutes a generic violation of cosmic censorship. We further discuss how this behavior is related to satellite formation in low-viscosity fluid streams subject to the Rayleigh-Plateau instability, and estimate the fractal dimension of the horizon prior to formation of the naked singularity.