AI 中文总结
该研究结合幂级数展开与数值计算，分析二次引力中满足特定对称性的旋转近视界极端解，确定极端旋转黑洞尺寸存在上限。
AI 中文摘要
结合幂级数展开与数值计算，分析二次引力的旋转近视界极端解。限于具有近视界极端克尔黑洞对称性（即具有$\boldsymbol{\text{AdS}_2}$结构）、球形视界拓扑及赤道反射对称性的几何，引入共形坐标简化爱因斯坦-外尔引力（即标量曲率为零的二次引力）的场方程。运用弗罗贝尼乌斯分析，对围绕赤道及极点展开的所有幂级数解进行分类，得到递推关系。借助数值分析，研究自由参数的微调以满足正则近视界极端几何的全局约束。对视界面积、视界标量曲率及旋转标量的计算显示，部分巴赫分支存在强烈的视界形变。此外，在有限视界面积之上不存在正则巴赫近视界几何，表明对应极端旋转黑洞的尺寸存在上限。
英文摘要
Rotating near-horizon extreme solutions of quadratic gravity are analyzed combining power series expansions and numerical calculations. Restricting to geometries with symmetries of the near-horizon extreme Kerr black hole (i.e., with the $\mathrm{AdS_2}$-structure), spherical horizon topology, and equatorial reflection symmetry, we introduce conformal coordinates simplifying the field equations of Einstein--Weyl gravity, i.e., quadratic gravity with vanishing scalar curvature. Employing the Frobenius analysis, we classify all power series solutions expanded around the equator as well as the poles, and obtain the recurrence relations. With the help of numerical analysis, we study fine-tuning of the free parameter to satisfy the global constraints on regular near-horizon extreme geometries. Computations of the horizon area, horizon scalar curvature, and rotational scalar reveal strong horizon deformations in some Bachian branches. Moreover, the absence of regular Bachian near-horizon geometries above a finite horizon area suggests an upper bound on the size of the corresponding extremal rotating black holes.
Comments8 pages, 6 figures
