Exterior Stability of Minkowski Space in Generalized Harmonic Gauge

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 met...

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Veröffentlicht in:Archive for rational mechanics and analysis 2023-10, Vol.247 (5), p.99, Article 99
1. Verfasser: Hintz, Peter
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-023-01931-3