On Scattering for Small Data of 2+1 Dimensional Equivariant Einstein-Wave Map System

TL;DR

This paper analyzes the long-term behavior of a coupled Einstein-wave map system in 2+1 dimensions, showing that certain subclasses disperse to linear equations, which is relevant for understanding 3+1 vacuum Einstein equations.

Contribution

It proves that two nonlinear subclasses of the 2+1 Einstein-wave map system disperse to their linearized counterparts, advancing understanding of their asymptotic behavior.

Findings

Two subclasses of the system disperse to linear equations

Global asymptotic behavior is characterized for the system

Relevance to 3+1 vacuum Einstein equations

Abstract

We consider the Cauchy problem of 2+1 equivariant wave maps coupled to Einstein's equations of general relativity and prove that two separate (nonlinear) subclasses of the system disperse to their corresponding linearized equations in the large. Global asymptotic behaviour of 2+1 Einstein-wave map system is relevant because the system occurs naturally in 3+1 vacuum Einstein's equations.