Generalized boundary conditions for general relativity for the asymptotically flat case in terms of Ashtekar's variables
Generalized boundary conditions for general relativity for the asymptotically flat case in terms of Ashtekar's variables
复制标题
根据 Ashtekar 变量的渐近平坦情况的广义相对论的广义边界条件
DOI：
10.1088/0264-9381/12/1/016
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发表时间：
1993
影响因子：
3.5
通讯作者：
T Thiemann
中科院分区：
文献类型：
--
作者：
T Thiemann
自从用 Ashtekar 的新变量表述广义相对论以来，存在一个尚未填补的空白，即处理渐近平场配置，这些配置足够通用，能够定义渐近庞加莱群的洛伦兹子群的生成元。虽然旧的几何动力学变量已经存在这样的公式，但到目前为止，只能定义平移子群的生成元，因为之前考虑的场的函数空间采用了过于特殊的形式。由于在空间无限处选择内部 SO(3) 框架的先验自由，并且由于在场和拉格朗日乘数上施加合适的边界条件时，Ashtekar 框架的非平凡现实条件重新进入舞台，因此框架从 ADM 变量到 Ashtekar 变量的转录并不是直截了当的。
There is a gap that has not been filled since the formulation of general relativity in terms of Ashtekar's new variables, namely the treatment of asymptotically flat field configurations that are general enough to be able to define the generators of the Lorentz subgroup of the asymptotic Poincaré group. While such a formulation already exists for the old geometrodynamical variables, up to now only the generators of the translation subgroup have been able to be defined, because the function spaces of the fields considered earlier are taken in too special a form. The transcription of the framework from the ADM variables to Ashtekar's variables turns out not to be straightforward, due to the a priori freedom to choose the internal SO(3) frame at spatial infinity, and due to the fact that the non-trivial reality conditions of the Ashtekar framework re-enter the stage when imposing suitable boundary conditions on the fields and the Lagrange multipliers.