Towards the Final Fate of an Unstable Black String

TL;DR

This study investigates the evolution and potential end-state of unstable black strings using numerical methods, revealing a tendency towards a chain of black holes connected by thin strings, but facing computational challenges in final analysis.

Contribution

The paper provides a numerical analysis of black string instability, exploring the dynamical evolution and intermediate configurations, which advances understanding beyond linear theory.

Findings

Black strings tend to form a sequence of black holes connected by thin strings.

Numerical simulations show rich dynamical behavior during evolution.

Computational difficulties prevent definitive determination of the final state.

Abstract

Black strings, one class of higher dimensional analogues of black holes, were shown to be unstable to long wavelength perturbations by Gregory and Laflamme in 1992, via a linear analysis. We revisit the problem through numerical solution of the full equations of motion, and focus on trying to determine the end-state of a perturbed, unstable black string. Our preliminary results show that such a spacetime tends towards a solution resembling a sequence of spherical black holes connected by thin black strings, at least at intermediate times. However, our code fails then, primarily due to large gradients that develop in metric functions, as the coordinate system we use is not well adapted to the nature of the unfolding solution. We are thus unable to determine how close the solution we see is to the final end-state, though we do observe rich dynamical behavior of the system in the intermediate stages.