Inverse Scattering on Asymptotically Hyperbolic Manifolds

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Scattering is defined on compact manifolds with boundary which are equipped with an asymptotically hyperbolic metric, $g.$ A model form is established for such metrics close to the boundary. It is shown that the scattering matrix at energy $ζ$ exists and is a pseudo-differential operator of order $2ζ+1 - \dim X.$ The symbol of the scattering matrix is then used to show that except for a countable set of energies the scattering matrix at one energy determines the diffeomorphism class of the metric modulo terms vanishing to infinite order at the boundary. An analogous result is proved for potential scattering. The total symbol is computed when the manifold is hyperbolic or is of product type modulo terms vanishing to infinite order at the boundary. The same methods are then applied to studying inverse scattering on the Schwarzschild and De Sitter-Schwarzschild models of black holes.

Keywords

Spectral Theory, Analysis of PDEs, 58G15

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/77740

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9811118
 http://arxiv.org/abs/math/9811118

Collections

arXiv