横向无迹张量的坐标无关表达式
Coordinate independent expression for transverse trace-free tensors
摘要：
非本征曲率的横向和无迹（TT）部分代表了$3 + 1$形式中引力场动力学自由度的一半。因此，它是数值相对论可自由指定的初始数据的一部分。虽然三维空间中的TT张量只有两个分量自由度，但它们通常不能仅由两个标量势给出。然而，对于平坦空间中的所有TT张量，已经以坐标形式导出了这样的表达式，这些张量也是平面对称或轴对称的（Conboye和Murchadha 2014 \emph{Class. Quantum Grav.} { \bf 31} 085019）。由于TT张量是共形协变的，这些也给出了共形平坦空间中的TT张量。本文推广了上述工作，给出了这些TT张量的坐标- \emph{independent}表达式。平移和轴对称条件也被推广到沿任何超曲面正交Killing向量的不变性。
英文摘要：
The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the $3 + 1$ formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT tensors in 3-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived however, in coordinate form, for all TT tensors in flat space which are also translationally or axially symmetric (Conboye and Ó Murchadha 2014 \emph{Class. Quantum Grav.} {\bf 31} 085019). Since TT tensors are conformally covariant, these also give TT tensors in conformally-flat space. In this article, the work above has been extended by giving a coordinate-\emph{independent} expression for these TT tensors. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
