On AdS Black Strings at Large $D$

In this paper we study the stability of an homogeneous black string in the presence of a negative cosmological constant with minimally coupled scalar fields by using the large $D$ effective theory. This method allows us to explore the dynamics of the black strings in the nonlinear regime. We find that up to the next-to-leading order of the $1/D$ expansion, the unique consistent solution of the equations of motion must be uniform. This means the recently found Gregory-Laflamme instability caused by fined-tuned non-generic perturbations would die out at late time in the evolution of the system.