Communications in Mathematical Physics

, Volume 321, Issue 1, pp 85–111 | Cite as

The Massive Wave Equation in Asymptotically AdS Spacetimes

Article

Abstract

We consider the massive wave equation on asymptotically AdS spaces. We show that the timelike \({\fancyscript{F}}\) behaves like a finite timelike boundary, on which one may impose the equivalent of Dirichlet, Neumann or Robin conditions for a range of (negative) mass parameter which includes the conformally coupled case. We demonstrate well posedness for the associated initial-boundary value problems at the H 1 level of regularity. We also prove that higher regularity may be obtained, together with an asymptotic expansion for the field near \({\fancyscript{F}}\). The proofs rely on energy methods, tailored to the modified energy introduced by Breitenlohner and Freedman. We do not assume the spacetime is stationary, nor that the wave equation separates.

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Physics, 4-183 CCISUniversity of AlbertaEdmontonCanada

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