Conformal Scattering of Maxwell Potentials

TL;DR

This paper develops a comprehensive conformal scattering theory for Maxwell potentials on curved, asymptotically flat spacetimes, including a novel gauge and a method to solve the characteristic Cauchy problem, extending to Minkowski space.

Contribution

It introduces a Lorenz-like gauge for Maxwell potentials on curved spacetimes, enabling a complete scattering theory and a new approach using the Morawetz vector field in Minkowski space.

Findings

Constructed a hyperbolic, non-singular gauge up to null infinity.

Developed a method to solve the characteristic Cauchy problem from scattering data.

Extended the scattering theory to Minkowski space with an alternative formulation.

Abstract

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 set of scattering data, we construct a Lorenz-like gauge which makes the field equations hyperbolic and non-singular up to null infinity, and reduces to an intrinsically solvable ODE on null infinity. We develop a method to solve the characteristic Cauchy problem from this scattering data based on a theorem of H\"ormander. In the case of Minkowski space, we further investigate an alternative formulation of the scattering theory by using the Morawetz vector field instead of the usual timelike Killing vector field.