The shear-free condition and constant-mean-curvature hyperboloidal initial data
The shear-free condition and constant-mean-curvature hyperboloidal initial data
复制标题
无剪切条件和恒定平均曲率双曲面初始数据
DOI：
10.1088/0264-9381/33/11/115015
复制
发表时间：
2015
影响因子：
3.5
通讯作者：
Iva Stavrov Allen
中科院分区：
文献类型：
--
作者：
P. Allen;J. Isenberg;John M. Lee;Iva Stavrov Allen
考虑Einstein-Maxwell流体约束方程，利用保角方法构造并参数化了满足无剪切条件的常平均曲率双曲面初始数据集。已知这个条件是必要的，以使时空发展在未来的零无穷远处允许一个规则的共形边界;参见（Andersson and Chruelciel 1994 Commun. 161 533-68）。我们使用各种正则类的初始数据集，主要考虑几何形状为弱渐近双曲的数据集，如（艾伦等人2015 arXiv：1506.03399）中所定义。这些度量是C1，1共形紧的，但不一定是C2共形紧的。为了确保我们构建的数据集确实是无剪切的，我们使用了在（艾伦等人2015 arXiv：1506.03399）中引入的共形协变无痕Hessian。此外，我们还构造了一类初始数据集的弱渐近双曲度量，可能只有C 0，1共形紧凑，这些数据集是不够正规，使无剪切条件的意义。
We consider the Einstein–Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is known to be necessary in order that a spacetime development admit a regular conformal boundary at future null infinity; see (Andersson and Chruściel 1994 Commun. Math. Phys. 161 533–68). We work with initial data sets in a variety of regularity classes, primarily considering those data sets whose geometries are weakly asymptotically hyperbolic, as defined in (Allen et al 2015 arXiv:1506.03399). These metrics are C1,1 conformally compact, but not necessarily C2 conformally compact. In order to ensure that the data sets we construct are indeed shear-free, we make use of the conformally covariant traceless Hessian introduced in (Allen et al 2015 arXiv:1506.03399). We furthermore construct a class of initial data sets with weakly asymptotically hyerbolic metrics that may be only C0,1 conformally compact; these data sets are insufficiently regular to make sense of the shear-free condition.
影响因子：
0.7
作者：
Allen, Paul T.;Isenberg, James;Lee, John M.;Stavrov Allen, Iva
通讯作者：
Stavrov Allen, Iva