全息相变附近柯西视界坍缩的临界卡斯纳标度
Critical Kasner scaling from Cauchy-horizon collapse near holographic phase transitions
- Beihang University（北京航空航天大学）
- Southeast University（东南大学）
- Shandong University（山东大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究揭示全息相变中临界零模通过对数分支控制柯西视界坍缩，并推导出卡斯纳标度与边界临界指数的关系，通过数值验证了该机制。
AI中文摘要：
我们研究了具有非极值柯西视界的稳态黑洞的连续标量毛分支。尽管外部形变在临界点消失，临界零模通常在参考柯西视界处产生对数分支，导致非均匀的临界极限。我们证明，标量扰动中对数项的系数与局部柯西视界数据一起决定了爱因斯坦-罗森桥的指数坍缩速率。如果坍缩后的几何演化进入卡斯纳区域，边界序参量标度$O\propto|\lambda-\lambda_c|^\beta$进一步意味着$1-p_t\propto|\lambda-\lambda_c|^{2\beta}$。关键的是，零模匹配固定了临界指数和相应的振幅，无需对非线性内部进行任何拟合。我们在从旋转BTZ到带毛旋转黑洞的转变中说明了这一机制。对于标量化的RN-AdS$_4$黑膜，我们使用完全非线性数值解定量验证了预测的卡斯纳标度。在低温下，具有相同线性临界数据的两个带电模型反而趋近于不同的红外端点，分别产生幂律和逆对数卡斯纳标度。因此，有限温度分岔附近的内部由零模传输控制，而低温标度则由非线性红外完备化主导。
英文摘要：
We study continuous scalar-hair bifurcations from stationary black holes with a nonextremal Cauchy horizon. Although the exterior deformation vanishes at criticality, the critical zero mode generically develops a logarithmic branch at the reference Cauchy horizon, producing a nonuniform critical limit. We show that the coefficient of this logarithm in the scalar perturbation, together with local Cauchy-horizon data, determines the exponential collapse rate of the Einstein-Rosen bridge. If the post-collapse geometry evolves into a Kasner regime, the boundary order-parameter scaling $O\propto|λ-λ_c|^β$ further implies $ 1-p_t\propto|λ-λ_c|^{2β}. $ Crucially, zero-mode matching fixes both the critical exponents and the associated amplitudes, without any fit to the nonlinear interior. We illustrate this mechanism in the transition from rotating BTZ to hairy rotating black holes. For scalarized RN-AdS$_4$ black branes, we quantitatively verify the predicted Kasner scaling using fully nonlinear numerical solutions. At low temperature, two charged models with identical linear critical data instead approach different infrared endpoints, yielding respectively power-law and inverse-logarithmic Kasner scaling. Thus interiors near a finite-temperature bifurcation are controlled by zero-mode transmission, whereas low temperature scaling is governed by the nonlinear infrared completion.
