Stringy Gregory-Laflamme

Thin enough black strings are unstable to rippling along their length, and the instability threshold indicates that static inhomogeneous black strings exist. These have indeed been constructed with increasing inhomogeneity until a high-curvature singular pinch appears. We study the string-scale version of this phenomenon: “string-ball strings”, which are linearly extended, self-gravitating configurations of string balls obtained within the Horowitz- Polchinski (HP) approach to near-Hagedorn string states. We construct inhomogeneous HP strings in spatial dimension d ≤ 6, and show that, as the inhomogeneity increases, they approach localized HP balls when d ≤ 5 or cease to exist when d = 6. We then discuss how string theory can smooth out the naked singularities that appear in the Kaluza-Klein black hole/black string transition, and we propose scenarios for the final stage of the evolution of the black string instability after string theory takes over.