Boundary conditions for isolated asymptotically anti-de Sitter spacetimes

We revisit the propagation of classical scalar fields in a spacetime, which is asymptotically anti-de Sitter. The lack of global hyperbolicity of the underlying background gives rise to an ambiguity in the dynamical evolution of solutions of the wave equation, requiring the prescription of extra boundary conditions at the conformal infinity to be fixed. We show that the only boundary conditions that are compatible with the hypothesis that the system is isolated, as defined by the (improved) energy–momentum tensor, are of Dirichlet and Neumann types.