标题： 静态球对称场配置的共线规范在对称平行引力中 显示英文标题

标题： Coincident gauge for static spherical field configurations in symmetric teleparallel gravity

摘要： 在对称的平行引力理论中，独立的联络由非度规性表征，而曲率和扭力为零，在这种情况下，可以找到一个坐标系，使得联络全局消失，协变导数简化为偏导数——即重合规范。 在本文中，我们推导出对于时空配置的通用变换规则，其中度规和联络都是静态且球对称的，并写出相应的重合规范度规形式。 通过在对称性和场方程允许的联络自由度中选择不同的方式，重合规范中的施瓦茨希尔德度规可以采取例如笛卡尔、Kerr-Schild 和对角（类似各向同性）形式，而在对称的平行标量-张量理论中的 BBMB 黑洞度规中，某种对角形式符合重合规范的要求，但笛卡尔和 Kerr-Schild 形式不符合。 不同的联络会导致边界项的不同值，这在原则上可能是物理相关的，但关于重合规范的简单论点似乎不足以唯一确定联络。 作为研究的副产品，我们还指出，只有静态球对称联络的一个特定子集在闵可夫斯基极限下具有消失的非度规性。 显示英文摘要

摘要： In symmetric teleparallel gravities, where the independent connection is characterized by nonmetricity while curvature and torsion are zero, it is possible to find a coordinate system whereby the connection vanishes globally and covariant derivatives reduce to partial derivatives -- the coincident gauge. In this paper we derive general transformation rules into the coincident gauge for spacetime configurations where the both the metric and connection are static and spherically symmetric, and write out the respective form of the coincident gauge metrics. Taking different options in fixing the freedom in the connection allowed by the symmetry and the field equations, the Schwarzschild metric in the coincident gauge can take for instance the Cartesian, Kerr-Schild, and diagonal (isotropic-like) forms, while the BBMB black hole metric in symmetric teleparallel scalar-tensor theory a certain diagonal form fits the coincident gauge requirements but the Cartesian and Kerr-Schild forms do not. Different connections imply different value for the boundary term which could in principle be physically relevant, but simple arguments about the coincident gauge do not seem to be sufficient to fix the connection uniquely. As a byproduct of the investigation we also point out that only a particular subset of static spherically symmetric connections has vanishing nonmetricity in the Minkowski limit.