The final state of black strings and p-branes, and the Gregory–Laflamme instability

Abstract

It is shown that the usual entropy argument for the Gregory–Laflamme (GL) instability for some appropriate black strings and p-branes gives surprising agreement up to a few per cent. This may provide strong support to GL's horizon fragmentation, which would produce the array of higher-dimensional Schwarzschild-type black holes finally. On the other hand, another estimator for the size of the black-hole end-state relative to the compact dimension indicates a second-order (i.e., smooth) phase transition for some other appropriate compactifications and total dimension of spacetime wherein the entropy argument is not appropriate. In this case, Horowitz–Maeda-type non-uniform black strings or p-branes can be the final state of the GL instability.