ar X iv : 0 70 6 . 36 69 v 1 [ m at h . A P ] 2 5 Ju n 20 07 THE WAVE EQUATION ON ASYMPTOTICALLY DE SITTER - LIKE SPACES
نویسنده
چکیده
In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds (X, g) which are de Sitterlike at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces. Under global assumptions on the (null)bicharacteristic flow, namely that the boundary of the compactification X is a union of two disjoint manifolds, Y±, and each bicharacteristic converges to one of these two manifolds as the parameter along the bicharacteristic goes to +∞, and to the other manifold as the parameter goes to −∞, we also define the scattering operator, and show that it is a Fourier integral operator associated to the bicharacteristic flow from Y+ to Y−.
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