title: Evolution and End Point of the Black String Instability: Large D Solution.
abstract: We derive a simple set of nonlinear, (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 nonuniform black strings. This proves an earlier conjecture about the end point of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly nonuniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the nonlinear dynamics of anti-de Sitter black branes at large D.
authors.affiliation: Institució Catalana de Recerca i Estudis Avançats (ICREA) Passeig Lluís Companys 23, E-08010 Barcelona, Spain.|Departament de Física Fonamental, Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.
authors.forename: Roberto
authors.initials: R
authors.lastname: Emparan
authors.affiliation: Department of Physics, Osaka City University, Osaka 558-8585, Japan.
authors.forename: Ryotaku
authors.initials: R
authors.lastname: Suzuki
authors.affiliation: Theory Center, Institute of Particles and Nuclear Studies, KEK, Tsukuba, Ibaraki 305-0801, Japan.
authors.forename: Kentaro
authors.initials: K
authors.lastname: Tanabe