Nonuniform black strings in various dimensions

TL;DR

This paper numerically constructs nonuniform black string solutions across dimensions 6 to 11, analyzing their physical properties and geometric features, and explores their behavior in the strongly non-linear regime.

Contribution

It provides the first detailed numerical analysis of nonuniform black strings in multiple dimensions, extending into the strongly non-linear regime and identifying geometric and physical characteristics.

Findings

Solutions are more massive and less entropic than the marginal string.

The local geometry near the waist is cone-like with less than 10% deviation.

The characteristic length scale follows a power-law dependence with a critical exponent.

Abstract

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.