AI 中文总结
本文建立了引力对称性与黑洞准正则模谱的关系，通过约化方案解决共形相关黑洞的等谱性矛盾，并应用于纯Weyl引力获得完整轴向谱。
AI 中文摘要
我们建立了引力理论对称性与黑洞（BH）准正则模（QNM）谱之间的一般关系。我们证明，当对称性在相应的QNM边值问题之间诱导双射时，该对称性意味着等谱性。然而，据报道，共形相关的黑洞表现出既依赖于共形因子又不依赖于共形因子的QNM谱。为解决这一问题，我们发展了一种高阶扰动方程的约化方案。将其应用于纯Weyl引力，得到了Schwarzschild的完整轴向谱，包括Regge-Wheeler和自旋-1分支。我们的结果表明，这些看似矛盾的结论源于扰动动力学或边界条件的差异。
英文摘要
We establish a general relation between symmetries of gravitational theories and black hole (BH) quasinormal mode (QNM) spectra. We show that a symmetry implies isospectrality when it induces a bijection between the corresponding QNM boundary value problems. However, conformally related BHs have been reported to exhibit both conformal factor dependent and independent QNM spectra. To resolve this issue, we develop a reduction scheme for higher order perturbation equations. Applied to pure Weyl gravity, it yields the complete axial spectrum of Schwarzschild, including Regge-Wheeler and spin-1 branches. Our results show that these seemingly contradictory conclusions result from differences in the perturbation dynamics or in the boundary conditions.
Comments9+6 pages
