On the Local Extension of the Future Null Infinity

TL;DR

This paper demonstrates the existence of solutions to the vacuum Einstein equations near a null cone, allowing the definition of a segment of future null infinity without small initial data assumptions.

Contribution

It extends the understanding of the Einstein equations by establishing solution existence around null cones with general decay, without requiring small initial data.

Findings

Solutions exist uniformly around the null cone

A segment of future null infinity can be defined

Initial data need not be small

Abstract

We consider a characteristic problem of the vacuum Einstein equations with part of the initial data given on a future complete null cone with suitable decay, and show that the solution exists uniformly around the null cone for general such initial data. We can then define a segment of the future null infinity. The initial data are not required to be small and the decaying condition inherits from the works of \cite{Ch-K} and \cite{K-N}.