The global stability of the Minkowski space-time in harmonic gauge

By Hans Lindblad, Igor Rodnianski. 2004

354 citations recorded by the source corpus.

We give a new proof of the global stability of Minkowski space originally established in the vacuum case by Christodoulou and Klainerman. The new approach shows that the Einstein-vacuum and the Einstein-scalar field equations with general asymptotically flat initial data satisfying a global smallness condition produce global (causally geodesically complete) solutions asymptotically convergent to the Minkowski space-time. The proof utilizes the classical harmonic (also known as de Donder or wave coordinate) gauge.

Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/40cbbb9229774fdc10f2c474a31209c471e4323c

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Citations in the corpus

On one-dimension semi-linear wave equations with null conditions (2017, background): “y on the special cancelations of the null form. We remark here that in R3+1 the null condition is a sucient but not necessary condition to obtain a small-data-global-existence result, see e.g. [11], [12]. For R2+1, the aforementioned classical null condition is not sucient to guarantee a small-data-”
The linear stability of the Schwarzschild solution to gravitational perturbations (2016, background): “Experience from non-linear problems, however, in particular the proof of the nonlinear stability of Minkowski space [13] referred to earlier (see also [44, 5]), indicates that (3a) and (3b) are naturally coupled.”
Extensions of the Stability Theorem of the Minkowski Space in General Relativity (2009, neutral): “Denote by T the following future-directed normal to this foliation: Tµ = −Φ2gµν∂νt.”
Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov) (2010, methodology): “On perturbations of Minkowski space itself, the full non-linear analysis was done in the path-breaking work of Christodoulou and Klainerman [9], and Lindblad and Rodnianski simplified the analysis [34, 35], Bieri [2, 3] succeeded in relaxing the decay conditions, while Wang [59] obtained additional,”