Evolution and endpoint of the black string instability: Large D solution

Understand

We derive a simple set of non-linear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D.

• These equations are easily solved numerically.
• Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable non-uniform black strings.
• This proves an earlier conjecture about the endpoint of the instability of black strings in a large enough number of dimensions.