AI 中文总结
本文推导了克尔黑洞稳态轴对称引力微扰中平均辐射规范与Weyl-Lewis-Papapetrou规范间的显式变换，将线性化WLP度规函数用Debye势表示，并通过实例验证了该重构程序。
AI 中文摘要
黑洞微扰的研究通常遵循两种主要方法：对度规进行直接微扰，或在Newman-Penrose（NP）形式体系或Geroch-Held-Penrose（GHP）形式体系内进行微扰。在后一种情况下，需要诸如基于Debye（赫兹）势的Chrzanowski-Cohen-Kegeles（CCK）方法之类的重构程序，以获得相应的度规微扰。然而，重构后的度规以辐射规范表示，该规范并不总是最优的。本文在两种框架内分析克尔黑洞的稳态轴对称微扰，聚焦于时空的真空部分（源外），推导平均辐射规范与度规取标准Weyl-Lewis-Papapetrou（WLP）形式的规范之间的显式规范变换，并将线性化WLP度规函数直接用Debye势表示。进一步讨论克尔黑洞向一般D型时空的微扰，并更详细地分析质量和角动量微扰。最后，通过两个超出D型类的示例说明该程序：薄盘对史瓦西黑洞的微扰，以及旋转粒子对克尔黑洞的微扰。
英文摘要
The study of black hole perturbations typically follows two main approaches: the direct perturbation of the metric, or the perturbation within the Newman-Penrose (NP) or Geroch-Held-Penrose (GHP) formalism. In the latter case, a reconstruction procedure, such as the Chrzanowski-Cohen-Kegeles (CCK) method based on the Debye (Hertz) potential, is required to obtain the corresponding metric perturbation. However, the reconstructed metric is then expressed in the radiation gauge, which is not always optimal. In this paper, we analyze stationary and axially symmetric perturbations of the Kerr black hole within both frameworks. Focusing on the vacuum part of the spacetime (outside the sources), we derive an explicit gauge transformation between the averaged radiation gauge and the gauge in which the metric takes its standard Weyl-Lewis-Papapetrou (WLP) form, and we express the linearized WLP metric functions directly in terms of the Debye potential. We further discuss perturbations of the Kerr black hole towards general type D spacetimes, and analyze the mass and angular momentum perturbations in more detail. Finally, we illustrate the procedure on two examples beyond the type D class: a perturbation of the Schwarzschild black hole by a thin disk, and a perturbation of the Kerr black hole by a rotating particle.
Comments17 pages, Acompanying Mathematica notebook: https://doi.org/10.5281/zenodo.21699521
