The Einstein-Klein-Gordon-AdS system for general boundary conditions

We construct unique local solutions for the spherically-symmetric Einstein-Klein-Gordon-AdS system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence. The proof relies on estimates developed for the linear wave equation by the second author and involves a careful renormalization of the dynamical variables, including a renormalization of the well-known Hawking mass. For some of the boundary conditions considered this system is expected to exhibit rich global dynamics, including the existence of hairy black holes. The present paper furnishes a starting point for such global investigations.