Stable Black Strings in Anti-de Sitter Space

TL;DR

This paper investigates the classical stability of five-dimensional anti-de Sitter black strings, finding conditions under which they are stable and discussing implications for the Gubser-Mitra conjecture.

Contribution

It demonstrates that AdS black strings can be stable if their horizon size exceeds the AdS radius, extending understanding of black string stability in curved spacetimes.

Findings

AdS black strings become stable when horizon size exceeds AdS radius

Unstable AdS black strings exhibit different fragmentation features from flat branes

Results have implications for the Gubser-Mitra conjecture

Abstract

In the five-dimensional Einstein gravity with negative cosmological constant in the presence/absence of a {\it non-fine-tuned} 3-brane, we have investigated the classical stability of black string solutions which are foliations of four-dimensional $AdS/dS$-Schwarzschild black holes. Such black strings are generically unstable as in the well-known Gregory-Laflamme instability. For $AdS$ black strings, however, it turns out that they become stable if the longitudinal size of horizon is larger than the order of the $AdS_4$ radius. Even in the case of unstable black strings, the $AdS$ black strings have a very different feature of string fragmentations from that in the flat brane world. Some implications of our results on the Gubser-Mitra conjecture are also discussed.