Global Nonlinear Stability of Large Dispersive Solutions to the Einstein Equations
Global Nonlinear Stability of Large Dispersive Solutions to the Einstein Equations
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DOI：
10.1007/s00023-021-01148-8
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
J. Luk;Sung-Jin Oh
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文献类型：
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作者：
J. Luk;Sung-Jin Oh
本文将Christodoulou-Klainerman关于Minkowski时空的全局非线性稳定性的重要结果推广到一类大色散时空的全局非线性稳定性。更准确地说，我们表明，任何定期未来因果测地线完整，渐近平坦的解决方案的爱因斯坦标量场系统，接近闵可夫斯基时空足够快的大的时间是未来的全球非线性稳定。结合Luk-Oh，Luk-Oh-Yang和Kilgore的结果，我们证明了Einstein标量场系统的一类大数据球对称色散解对于非球对称小扰动是全局非线性稳定的.这，特别是，给出了第一个建设的一个开放的一组大的渐近平坦的初始数据的解决方案，爱因斯坦标量场系统是未来因果测地线完成。
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.