Non-uniform black strings in various dimensions

The nonuniform black strings branch, which emerges from the critical Gregory-Laflamme string, is numerically constructed in dimensions 6 <= D <= 11 and extended into the strongly non-linear regime. All the solutions are more massive and less entropic than the marginal string. We find the asymptotic values of the mass, the entropy and other physical variables in the limit of large horizon deformations. By explicit metric comparison we verify that the local geometry around the ``waist'' of our most nonuniform solutions is cone-like with less than 10% deviation. We find evidence that in this regime the characteristic length scale has a power-law dependence on a parameter along the branch of the solutions, and estimate the critical exponent