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In this paper we study the stability of an homogeneous black string in thepresence of a negative cosmological constant with minimally coupled scalarfields by using the large $D$ effective theory. This method allows us toexplore the dynamics of the black strings in the nonlinear regime. We find thatup to the next-to-leading order of the $1/D$ expansion, the unique consistentsolution of the equations of motion must be uniform. This means the recentlyfound Gregory-Laflamme instability caused by fined-tuned non-genericperturbations would die out at late time in the evolution of the system.

On AdS Black Strings at Large $D$