, Volume 321, Issue 1, pp 85-111
Date: 03 May 2013

The Massive Wave Equation in Asymptotically AdS Spacetimes

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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.