Gregory-Laflamme instability of 5D electrically charged black strings

TL;DR

This paper investigates how electric charge affects the stability of five-dimensional black strings, finding that increased charge reduces their stability through numerical analysis of perturbations.

Contribution

It provides a detailed analysis of the Gregory-Laflamme instability for charged black strings, deriving the master equation and critical parameters using numerical methods.

Findings

Electric charge decreases black string stability.

Critical wavelength for instability depends on charge.

Phase diagram illustrates stability regions.

Abstract

We study the Gregory-Laflamme instability of 5D compactified, electrically charged black strings. We consider static, linear perturbations of these solutions and derive master equation for these perturbations. Using numerical analysis we search for the threshold unstable modes and derive the critical wave-length. The results are illustrated in the black string mass v.s. electric charge phase diagram. Similar diagram is constructed using global thermodynamic equilibrium argument applied to the charged string and 5D electrically charged black hole. The results derived illustrate that electric charge makes the black string less stable.