论文标题
改进了黑洞超高分析解决方案
Improved Analytic Solution of Black Hole Superradiance
论文作者
论文摘要
klein-gordon方程对质量$ $ $的真实标量场的近似解决方案在detweiler \ cite {detweiler：1980uk}获得的Kerr黑洞的几何形状中，广泛用于黑孔的稳定性，以及对轴突类颗粒的搜索。在这项工作中，我们在此解决方案中确认了缺少因子$ 1/2 $，该因素首先在参考文献〜\ cite {pani：2012bp}中确定。校正后的结果具有奇怪的功能，可以提出问题计数策略。我们通过添加近代领先顺序（NLO）贡献来解决此问题。与数值结果相比，对于所有重要值$r_gμ$ $，NLO解决方案将LO解的百分比误差降低了2倍。尤其是百分比误差是$ \ lyssim 10 \％$在$r_gμ\ Lessim 0.35 $的区域中。 NLO溶液还具有紧凑的形式，可以直接使用。
The approximate solution of the Klein-Gordon equation for a real scalar field of mass $μ$ in the geometry of a Kerr black hole obtained by Detweiler \cite{Detweiler:1980uk} is widely used in the analysis of the stability of black holes as well as the search of axion-like particles. In this work, we confirm a missing factor $1/2$ in this solution, which was first identified in Ref.~\cite{Pani:2012bp}. The corrected result has strange features that put questions on the power-counting strategy. We solve this problem by adding the next-to-leading order (NLO) contribution. Compared to the numerical results, the NLO solution reduces the percentage error of the LO solution by a factor of 2 for all important values of $r_g μ$. Especially the percentage error is $\lesssim 10\%$ in the region of $r_gμ\lesssim 0.35$. The NLO solution also has a compact form and could be used straightforwardly.
