Boundary conditions for isolated asymptotically anti-de Sitter spacetimes

TL;DR

This paper investigates the boundary conditions necessary for well-defined scalar field evolution in asymptotically anti-de Sitter spacetimes, establishing that only Dirichlet and Neumann conditions are compatible with the system being isolated.

Contribution

It clarifies the permissible boundary conditions for scalar fields in asymptotically AdS spacetimes ensuring physical consistency and isolation.

Findings

Only Dirichlet and Neumann boundary conditions are compatible with the system being isolated.

The lack of global hyperbolicity necessitates boundary conditions at conformal infinity.

The study refines understanding of boundary conditions in AdS spacetime physics.

Abstract

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 tha are compatible with the hypothesis that the system is isolated, as defined by the (improved) energy-momentum tensor, are of Dirichlet and Neumann types.