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

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

2011-03-03

arxiv.org/abs/1103.0710v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, to appear in JHDE

Scientific paper

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).

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