Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship

TL;DR

This paper investigates the nonlinear evolution of 5-dimensional black strings under Gregory-Laflamme instability, revealing a cascade process leading to naked singularities and demonstrating a generic violation of cosmic censorship.

Contribution

It provides the first detailed simulation of nonlinear black string dynamics showing a self-similar cascade and cosmic censorship violation.

Findings

Black strings undergo a Gregory-Laflamme instability leading to a cascade of smaller black holes.

The horizon dynamics resemble fluid instabilities like Rayleigh-Plateau.

Simulations suggest the formation of naked singularities in finite time.

Abstract

We describe the behavior of 5-dimensional black strings, subject to the Gregory-Laflamme instability. Beyond the linear level, the evolving strings exhibit a rich dynamics, where at intermediate stages the horizon can be described as a sequence of 3-dimensional spherical black holes joined by black string segments. These segments are themselves subject to a Gregory-Laflamme instability, resulting in a self-similar cascade, where ever-smaller satellite black holes form connected by ever-thinner string segments. This behavior is akin to satellite formation in low-viscosity fluid streams subject to the Rayleigh-Plateau instability. The simulation results imply that the string segments will reach zero radius in finite asymptotic time, whence the classical space-time terminates in a naked singularity. Since no fine-tuning is required to excite the instability, this constitutes a generic violation of cosmic censorship.