Gregory-Laflamme instability of 5D electrically charged black strings

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.