A generalization of the propagation of singularities theorem on asymptotically anti‐de Sitter spacetimes

Claudio Dappiaggi and Alessio Marta

Mathematische Nachrichten, 2022, vol. 295, issue 10, 1934-1968

Abstract: In a recent paper O. Gannot and M. Wrochna considered the Klein–Gordon equation on an asymptotically anti‐de Sitter spacetime subject to Robin boundary conditions, proving in particular a propagation of singularities theorem. In this work we generalize their result considering a more general class of boundary conditions implemented on the conformal boundary via pseudodifferential operators of suitable order. Using techniques proper of b‐calculus and of twisted Sobolev spaces, we prove also for the case in hand a propagation of singularity theorem along generalized broken bicharacteristics, highlighting the potential presence of a contribution due to the pseudodifferential operator encoding the boundary condition.

Date: 2022
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