Kerr-AdS$_5$黑洞的复相结构：临界鞍点与Fisher零点
Complex Phase Structure of Kerr-AdS$_5$ Black Holes: Critical Saddles and Fisher Zeros
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中文总结 AI 辅助
本文研究单旋转Kerr-AdS$_5$黑洞的复鞍点结构，发现小大黑洞鞍点合并与Hawking-Page相变不同，Fisher零点在共存线附近累积，且满足KSW相位界，区分了局部简并与全局相共存。
中文摘要 AI 辅助
我们利用固定角速度$\Omega$的大正则系综中的双变量约化模型，研究了单旋转Kerr--AdS$_5$黑洞的复鞍点结构。小黑洞和大黑洞鞍点在临界点处合并，此时复Hessian的一个Takagi奇异值为零，从而识别出与合并相关的软模。在整个物理域$|\Omega|<1$内，这种合并始终不同于Hawking--Page相变。对于具有标准测度的约化积分，我们证明当牛顿常数$G$足够小时，热AdS在每一个实合并点的复邻域内均匀地占主导地位。因此，尽管局部鞍点合并由Airy型行为描述，该邻域内不包含配分函数的零点。相反，Fisher零点通过热AdS与大数据黑洞鞍点之间的干涉，在Hawking--Page共存线附近累积，其间距量级为$G$。我们还证明了实拟欧几里得Kerr--AdS$_5$族在$|\Omega|<1$时满足严格的渐近Kontsevich--Segal--Witten（KSW）相位界，且合并点位于允许域内。在固定角动量的扩展系综中，两个这样的合并点结合成一个尖点，并伴随依赖于轮廓的Pearcey近似。这些结果将局部鞍点简并性与全局相共存区分开来，并阐明了Takagi模、相变和配分函数零点在复杂黑洞鞍点结构中的不同作用。
英文摘要
We study the complex saddle structure of singly rotating Kerr--AdS$_5$ black holes using a two-variable reduced model in the grand canonical ensemble at fixed angular velocity, $Ω$. The small and large black hole saddles merge at a critical point where one Takagi singular value of the complex Hessian vanishes, identifying the soft mode associated with the merger. This merger remains distinct from the Hawking--Page transition throughout the physical domain $|Ω| < 1$. For the reduced integral with the standard measure, we show that thermal AdS dominates uniformly in a complex neighborhood of each real merger point when Newton's constant $G$ is sufficiently small. Consequently, this neighborhood contains no zeros of the partition function, even though the local saddle merger is described by Airy-type behavior. The Fisher zeros instead accumulate near the Hawking--Page coexistence line, with spacing of order $G$, through interference between thermal AdS and the large black hole saddle. We also show that the real quasi-Euclidean Kerr--AdS$_5$ family satisfies a strict asymptotic Kontsevich--Segal--Witten (KSW) phase bound for $|Ω| < 1$, with the merger point lying inside the allowed domain. In the fixed angular momentum extended ensemble, two such merger points combine into a cusp with a contour-dependent Pearcey approximation. These results distinguish local saddle degeneracies from global phase coexistence and clarify the different roles of Takagi modes, phase transitions, and zeros of the partition function in the complex black hole saddle structure.
发表机构
- Sogang University（西江大学）
- Shanghai University（上海大学）
- Dongguk University（东国大学）
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