arXiv 2011.139552020-11gr-qc

几乎Killing方程的扰动及其意义

Perturbations of the almost Killing equation and their implications

Sumanta Chakraborty, Justin C. Feng

备注：: 21 pages. Matches published version
发表信息：: Phys. Rev. D 103, 084020 (2021)
DOI：: 10.1103/PhysRevD.103.084020

摘要：

杀死矢量在描述给定时空的对称性方面起着至关重要的作用。然而，现实的天体物理系统在大多数情况下只是近似对称的。即使在天体物理学的黑洞中，人们也可能认为由于外部物质场的扰动，基灵对称性只在近似意义上存在。在这项工作中，我们考虑了由几乎Killing方程提供的Killing向量的广义概念，并研究了由满足精确Killing对称性的背景时空的扰动引起的扰动。到一阶，我们证明了对称真空时空的非辐射度量扰动（即，非零迹的度量扰动），扰动几乎Killing方程避免了双曲参数选择的无界哈密顿量的问题。对于无痕度量扰动，我们得到了类似的结果，几乎Killing方程的二阶扰动，与一些额外的警告。热力学的影响也进行了探讨。

英文摘要：

Killing vectors play a crucial role in characterizing the symmetries of a given spacetime. However, realistic astrophysical systems are in most cases only approximately symmetric. Even in the case of an astrophysical black hole, one might expect Killing symmetries to exist only in an approximate sense due to perturbations from external matter fields. In this work, we consider the generalized notion of Killing vectors provided by the almost Killing equation, and study the perturbations induced by a perturbation of a background spacetime satisfying exact Killing symmetry. To first order, we demonstrate that for nonradiative metric perturbations (that is, metric perturbations with nonvanishing trace) of symmetric vacuum spacetimes, the perturbed almost Killing equation avoids the problem of an unbounded Hamiltonian for hyperbolic parameter choices. For traceless metric perturbations, we obtain similar results for the second-order perturbation of the almost Killing equation, with some additional caveats. Thermodynamical implications are also explored.

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