Exterior stability of Minkowski space in generalized harmonic gauge

Autor:	Hintz, Peter
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs General Relativity and Quantum Cosmology Primary: 35B40 Secondary: 83C05 35L05
Druh dokumentu:	Working Paper
Popis:	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. Comment: 36 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.13804 Zobrazit plný text záznamu View this record from Arxiv