发表机构
Yantai University; Institute of Frontier and Interdisciplinary Science, Shandong University（烟台大学; 山东大学前沿交叉科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究全息超导体临界行为如何控制带电黑洞内部几何，发现临界零模决定爱因斯坦-罗森坍缩宽度和约瑟夫森相位，并影响Kasner纪元，低温行为则由红外端点控制。
AI 中文摘要
我们研究了全息超导体的临界行为如何控制带电黑洞的内部几何结构。尽管外部凝聚在临界点消失，但临界零模在Reissner--Nordström柯西视界附近发展出对数振荡，使得内部临界极限变得非均匀。我们证明了透射的临界模振幅与局部柯西视界量一起，决定了后续约瑟夫森区域中领先的爱因斯坦--罗森坍缩宽度$\Delta z_{\rm ER}$和相位$\Theta_J$。如果凝聚满足$t\equiv1-T/T_c\propto\epsilon^{2r}$，则$\Delta z_{\rm ER}\propto t^{1/r}$且$\Theta_J\propto t^{-1/r}$。该约瑟夫森相位被转移到第一个Kasner纪元，产生振荡的Kasner指数以及标量速度连续零点满足的累积律$t_n\sim n^{-r}$。临界零模确定了领先的坍缩和相位系数，这些系数在普通和三临界情形下均被完全非线性解定量证实。在低温下，内部结构反而依赖于零温几何的红外完备化。因此，近临界标度由临界模透射控制，而低温行为由红外端点控制。
英文摘要
We study how the critical behavior of holographic superconductors controls the interior geometry of charged black holes. Although the exterior condensate vanishes at criticality, the critical zero mode develops logarithmic oscillations near the Reissner--Nordström Cauchy horizon, rendering the interior critical limit nonuniform. We show that the transmitted critical-mode amplitude, together with local Cauchy-horizon quantities, fixes both the leading Einstein--Rosen collapse $Δz_{\rm ER}$ width and the phase $Θ_J$ in the subsequent Josephson regime. If the condensate obeys $t\equiv1-T/T_c\proptoε^{2r}$, then $Δz_{\rm ER}\propto t^{1/r}$ and $Θ_J\propto t^{-1/r}$. This Josephson phase is transferred to the first Kasner epoch, producing oscillatory Kasner exponents and an accumulation law $t_n\sim n^{-r}$ for successive zeros of the scalar velocity. The critical zero mode fixes the leading collapse and phase coefficients, which are quantitatively confirmed by fully nonlinear solutions in both the ordinary and tricritical cases. At low temperature, the interior instead depends on the infrared completion of the zero-temperature geometry. Thus near-critical scaling is governed by critical-mode transmission, whereas the low-temperature behavior is controlled by the infrared endpoint.
Comments37 pages + appendices, 20 figures
