1202.3445 (C. M. Warnick)

The massive wave equation in asymptotically AdS spacetimes    [PDF]

C. M. Warnick

We consider the massive wave equation on asymptotically AdS spaces. We show
that the timelike scri 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 scri. 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.

View original: http://arxiv.org/abs/1202.3445