Well-posedness for the massive wave equation on asymptotically anti-de Sitter spacetimes

TL;DR

This paper proves the well-posedness of the massive wave equation on asymptotically anti-de Sitter spacetimes, establishing existence, uniqueness, and the construction of solutions via boundary limits.

Contribution

It provides the first rigorous proof of well-posedness for the massive wave equation in this setting, with solutions constructed as limits of boundary value problems.

Findings

Solution exists and is unique within the energy class.

Solutions can be obtained as limits of boundary value problems.

Uniqueness fails if decay at infinity is weakened.

Abstract

In this short paper, we prove a well-posedness theorem for the massive wave equation (with the mass satisfying the Breitenlohner-Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class (but non-unique if the decay at infinity is weakened).