# Exterior stability of Minkowski space in generalized harmonic gauge

## TL;DR

This paper proves the existence of a small null infinity region in certain Einstein vacuum spacetimes by modifying harmonic gauges to ensure decay at infinity, using geometric analysis techniques.

## Contribution

It introduces a new gauge modification and a constraint damping formulation to establish decay and existence results for Einstein vacuum equations.

## Key findings

- Existence of a small null infinity region in asymptotically flat spacetimes.
- A new gauge condition ensures strong decay at null infinity.
- Streamlined proof of semiglobal existence using geometric singular analysis.

## Abstract

We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the standard wave coordinate gauge in which all non-physical metric degrees of freedom have strong decay at null infinity. Using a formulation of the gauge-fixed Einstein vacuum equations which implements constraint damping, we establish this strong decay regardless of the validity of the constraint equations. On a technical level, we use notions from geometric singular analysis to give a streamlined proof of semiglobal existence for the relevant quasilinear hyperbolic equation.