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

Abstract

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. If the initial black string is very thin, the final configuration is highly non-uniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the non-linear dynamics of Anti-deSitter black branes at large D.

8 pages, 2 figures. v2: slightly more general equations and other small improvements

References in corpus (9)

• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Instabilities of Black Strings and Branes
• Effective theory of Black Holes in the 1/D expansion
• A membrane paradigm at large D
• High and Low Dimensions in The Black Hole Negative Mode
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
• Non-uniform black strings and the critical dimension in the $1/D$ expansion
• Stationary black holes: Large $D$ analysis

Cited by in corpus (67)

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