论文标题
方便轴向对称性病毒身份的方便量表
A convenient gauge for virial identities in axial symmetry
论文作者
论文摘要
病毒身份是一般相对论中有用的数学工具。它们不仅被用作数值精度工具，而且还可以从能量平衡的角度对所考虑的系统进行一些物理洞察力，在建立无行为和无发品定理中发挥了重要作用。尽管这些身份的计算往往是德里克缩放参数〜\ cite {derrick1964comments}的直接应用，但所产生的身份的复杂性取决于系统。特别是，由于指标函数的二阶导数，爱因斯坦 - 希尔伯特作用的贡献变得越来越复杂。此外，需要考虑到gibbons-hawking-york术语\ cite {herdeiro：2021teo}。值得庆幸的是，由于重力作用仅取决于度量，因此预计存在一个``方便''仪表，使重力作用贡献存在。尽管在球形对称性中已经知道了这样的仪表（$ m-σ$ apartretization），但轴向对称性尚未发现。在这封信中，我们提出了一个``方便''仪表用于轴向对称性，并使用它来计算带有标量头发的Kerr黑洞的身份。
Virial identities are a useful mathematical tool in General Relativity. Not only have they been used as a numerical accuracy tool, but they have also played a significant role in establishing no-go and no-hair theorems while giving some physical insight into the considered system from an energy balance perspective. While the calculation of these identities tends to be a straightforward application of Derrick's scaling argument~\cite{derrick1964comments}, the complexity of the resulting identity is system dependent. In particular, the contribution of the Einstein-Hilbert action, due to the presence of second-order derivatives of the metric functions, becomes increasingly complex for generic metrics. Additionally, the Gibbons-Hawking-York term needs to be taken into account \cite{Herdeiro:2021teo}. Thankfully, since the gravitational action only depends on the metric, it is expected that a ``convenient'' gauge that trivializes the gravitational action contribution exists. While in spherical symmetry such a gauge is known (the $m-σ$ parametrization), such has not been found for axial symmetry. In this letter, we propose a ``convenient'' gauge for axial symmetry and use it to compute an identity for Kerr black holes with scalar hair.
