Related papers: Conformal scattering of the wave equation in the V…
The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities.…
In this paper, we establish a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime. We combine the energy and pointwise decay results for solutions obtained in \cite{Yang} with a Sobolev embedding…
We construct a complete conformal scattering theory for Maxwell fields in the static exterior region of a Reissner-Nordstr{\o}m-de Sitter black bole spacetime. This is done using uniform energy decay results that we obtain in a separate…
We show that existing decay results for scalar fields on the Schwarzschild metric are sufficient to obtain a conformal scattering theory. Then we re-interpret this as an analytic scattering theory defined in terms of wave operators, with an…
We investigate the geometrical structure of Vaidya's spacetime in the case of a white hole with decreasing mass, stabilising to a black hole in finite or infinite time or evaporating completely. Our approach relies on a detailed analysis of…
We investigate to construct a conformal scattering theory of the spin-$1/2$ massless Dirac equation on the Kerr spacetime by using the conformal geometric method and under an assumption on the pointwise decay of the Dirac field. In…
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the…
In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.
In this paper, we establish the constructions of conformal scattering theories for the tensorial wave equation such as the tensorial Fackerell-Ipser and the spin $\pm 1$ Teukolsky equations on Schwarzschild spacetime. In our strategy, we…
The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data,…
An integral equation method for scalar scattering in Schwarzschild spacetime is constructed. The zeroth-order and first-order scattering phase shift is obtained.
The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. We derive an integral spectral representation for the solution and prove pointwise decay in time.
We provide in this paper a first step to obtain the conformal scattering theory for the linearized gravity fields on the Schwarzschild spacetime by using the conformal geometric approach. We will show that the existing decay results for the…
We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…
We study the scalar, conformally invariant wave equation on a four-dimensional Minkowski background in spherical symmetry, using a fully pseudospectral numerical scheme. Thereby, our main interest is in a suitable treatment of spatial…
We study solutions to the linear wave equation on the cosmological region of Schwarzschild-de Sitter spacetimes. We show that all sufficiently regular finite-energy solutions to the linear equation possess a particular finite-order…
We discuss the near singularity region of the linear mass Vaidya metric. In particular we investi- gate the structure in the numerical solutions for the scattering of scalar and electromagnetic metric perturbations from the singularity. In…
This thesis is concerned with the development and application of conformal techniques to numerical calculations of asymptotically flat spacetimes. The conformal compactification technique enables us to calculate spatially unbounded domains,…
We study the peeling for the wave equation on the Vaidya spacetime following the approach developed by Mason and Nicolas in Mason-Nicolas 2009. The idea is to encode the regularity at null infinity of the rescaled field, characterised by…
We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full…