General Relativistic Scalar Field Models in the Large

TL;DR

This paper proves the existence and uniqueness of solutions for certain scalar field models in general relativity, demonstrating their asymptotic flatness and regularity at infinity using conformal techniques.

Contribution

It establishes a new equivalence between hyperboloidal initial value problems and conformal methods for scalar fields in general relativity.

Findings

Unique solutions are proven to exist for the hyperboloidal initial value problem.

Solutions are weakly asymptotically flat with smooth future null infinity.

For near-flat initial data, solutions exhibit regular future timelike infinity.

Abstract

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.