Resolvents, Poisson operators and scattering matrices on asymptotically hyperbolic and de Sitter spaces

TL;DR

This paper explores the relationship between operators on different asymptotic geometries, specifically hyperbolic and de Sitter spaces, and computes the scattering operator linking these geometries.

Contribution

It introduces a method to relate boundary operators on asymptotically Minkowski spaces to hyperbolic and de Sitter spaces, and explicitly computes the associated scattering operator.

Findings

Established a link between boundary operators on different asymptotic geometries

Computed the scattering operator in terms of constituent scattering operators

Provided a framework for analyzing wave propagation on complex geometric backgrounds

Abstract

We describe how the global operator induced on the boundary of an asymptotically Minkowski space links two asymptotically hyperbolic spaces and an asymptotically de Sitter space, and compute the scattering operator of the linked problem in terms of the scattering operator of the constituent pieces.