Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2021-01-01 , DOI: 10.1007/s00023-020-00990-6 Paul T. Allen , James Isenberg , John M. Lee , Iva Stavrov Allen
We present a procedure for asymptotic gluing of hyperboloidal initial data sets for the Einstein field equations that preserves the shear-free condition. Our construction is modeled on the gluing construction in Isenberg et al. (Ann Henri Poincaré 11(5):881–927, 2010), but with significant modifications that incorporate the shear-free condition. We rely on the special Hölder spaces, and the corresponding theory for elliptic operators on weakly asymptotically hyperbolic manifolds, introduced by the authors in Allen et al. (Commun Anal Geom 26(1):1–61, 2018) and applied to the Einstein constraint equations in Allen et al. (Class Quantum Grav 33(11):115015, 2016).
中文翻译:
无剪切双曲面初始数据集的渐近粘合
我们为爱因斯坦场方程提供了双曲线初始数据集的渐近粘合过程,该过程保留了无剪切条件。我们的结构以Isenberg等人的粘合结构为模型。(安·亨利·庞加莱(Ann HenriPoincaré)11(5):881–927,2010年),但进行了重大修改,纳入了无剪切条件。我们依赖于特殊的Hölder空间以及弱渐近双曲流形上椭圆算子的相应理论,作者在Allen等人的文章中对此进行了介绍。(Commun Anal Geom 26(1):1-61,2018),并应用于Allen等人的爱因斯坦约束方程。(Class Quantum Grav 33(11):115015,2016)。