论文标题
变形的schwarzschild黑洞的艾科纳尔准模式和光子轨道
Eikonal quasinormal modes and photon orbits of deformed Schwarzschild black holes
论文作者
论文摘要
几何光学近似提供了艾科纳尔对应关系的解释，在含黑色孔的空间中，将高频黑洞准模式与所说的黑洞围绕着封闭的光子轨道连接。 Schwarzschild，Reissner-Nordström，Kerr和Kerr-Newman黑洞已明确确定了这种通信，这可能是对一般相对性超出物理学的潜在提示。值得注意的是，上述黑洞的空间具有足够的对称性，因此地球方程和主波方程都是可分开的。对应关系的识别似乎在很大程度上取决于这些对称性。一个人自然地询问如果时空不太对称，则如何出现艾科纳尔对应关系。为了朝这个方向进行开创性的工作，我们在本文中考虑了变形的Schwarzschild时空，仅保持轴对称和平稳性。我们证明，到时空变形的一阶，Eikonal对应关系通过\ textit {均值{平均}半径沿其一个时期的\ textit {均值}半径的定义表现出来。该平均半径与主波方程中的电势峰重叠，可以将其定义为时空变形的第一阶，从而明确识别艾科纳尔对应关系。
The geometric optics approximation provides an interpretation for eikonal correspondence that, in black-hole-containing spacetimes, connects high-frequency black hole quasinormal modes with closed photon orbits around said black hole. This correspondence has been identified explicitly for Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman black holes, the violation of which can be a potential hint toward physics beyond General Relativity. Notably, the aforementioned black hole spacetimes have sufficient symmetries such that both the geodesic equations and the master wave equations are separable. The identification of the correspondence seems to largely rely on these symmetries. One naturally asks how the eikonal correspondence would appear if the spacetime were less symmetric. For a pioneering work in this direction, we consider in this paper a deformed Schwarzschild spacetime retaining only axisymmetry and stationarity. We show that up to the first order of spacetime deformations the eikonal correspondence manifests through the definition of the \textit{averaged} radius of trapped photon orbits along their one period. This averaged radius overlaps the potential peak in the master wave equation, which can be defined up to the first order of spacetime deformations, allowing the explicit identification of the eikonal correspondence.
