On the existence and convergence of polyhomogeneous expansions of zero-rest-mass fields

TL;DR

This paper proves the existence and convergence of polyhomogeneous expansions for zero-rest-mass fields in asymptotically flat spacetimes, using auxiliary fields and symmetric hyperbolic systems.

Contribution

It introduces a method to establish existence of solutions for polyhomogeneous zero-rest-mass fields by transforming the problem into regular initial value problems.

Findings

Existence of solutions for the asymptotic characteristic initial value problem.

Polyhomogeneous expansions converge in asymptotically flat spacetimes.

Auxiliary fields enable the application of symmetric hyperbolic system techniques.

Abstract

The convergence of polyhomogeneous expansions of zero-rest-mass fields in asymptotically flat spacetimes is discussed. An existence proof for the asymptotic characteristic initial value problem for a zero-rest-mass field with polyhomogeneous initial data is given. It is shown how this non-regular problem can be properly recast as a set of regular initial value problems for some auxiliary fields. The standard techniques of symmetric hyperbolic systems can be applied to these new auxiliary problems, thus yielding a positive answer to the question of existence in the original problem.