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arXiv · 2108.13379

Global nonlinear stability of large dispersive solutions to the Einstein equations

Jonathan Luk·Sung-Jin Oh
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Abstract

We extend the monumental result of Christodoulou-Klainerman on the global nonlinear stability of the Minkowski spacetime to the global nonlinear stability of a class of large dispersive spacetimes. More precisely, we show that any regular future causally geodesically complete, asymptotically flat solution to the Einstein-scalar field system which approaches the Minkowski spacetime sufficiently fast for large times is future globally nonlinearly stable. Combining our main theorem with results of Luk-Oh, Luk-Oh-Yang and Kilgore, we prove that a class of large data spherically symmetric dispersive solutions to the Einstein-scalar field system are globally nonlinearly stable with respect to small non-spherically symmetric perturbations. This in particular gives the first construction of an open set of large asymptotically flat initial data for which the solutions to the Einstein-scalar field system are future causally geodesically complete.

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Jonathan Luk, Sung-Jin Oh. 2021-08-30. Global nonlinear stability of large dispersive solutions to the Einstein equations. https://doi.org/10.1007/s00023-021-01148-8

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