将引力涨落投影到近视界喉道
Projecting Gravitational Fluctuations onto Near-Horizon Throats
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中文总结 AI 辅助
针对线性化涨落方程可分离为Heun方程的静态几何，利用微分同胚将引力涨落问题投影为耦合等谱高斯超几何问题，推导相关结果并识别黑洞模式与特定泛函空间基的对应关系。
中文摘要 AI 辅助
我们证明，对于线性化涨落方程可分离为径向和角向Heun方程的静态几何，一对微分同胚可将整个问题投影到互补时空区域中的两个耦合、等谱的高斯超几何问题。该投影要求在互补区域的交界面施加Robin边界条件，且这些条件可通过要求两个微分同胚在该交界面匹配唯一确定。该方法独立推导了近期从Heun连接系数与Nekrasov-Shatashvili极限下瞬子配分函数对应关系得到的结果。作为应用，我们在克尔-德西特和克尔-反德西特黑洞中识别出一组模式，在近极端极限下，这些模式可连续约化为引力涨落的Schwarzian/Jackiw-Teitelboim泛函空间的基。
英文摘要
We show that, for stationary geometries whose linearized fluctuation equations separate into radial and angular Heun equations, a pair of diffeomorphisms projects the full problem onto two coupled, isospectral Gauss hypergeometric problems in complementary spacetime regions. This projection requires Robin boundary conditions to be imposed at the intersection between the complementary regions, which are uniquely fixed by requiring the two diffeomorphisms to match there. The method provides an independent derivation of recent results obtained from the correspondence between Heun connection coefficients and instanton partition functions in the Nekrasov-Shatashvili limit. As an application, we identify a subset of modes in Kerr-de Sitter and Kerr-anti-de Sitter black holes that, in the near-extremal limit, continuously reduce to a basis of the Schwarzian/Jackiw-Teitelboim functional space of gravitational fluctuations.
