From Critical Zero Modes to Interior Dynamics in Holographic Superconductors
Abstract
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 ΔzER width and the phase ΘJ in the subsequent Josephson regime. If the condensate obeys t≡1−T/Tc∝ε2r, then ΔzER∝ t1/r and ΘJ∝ t−1/r. This Josephson phase is transferred to the first Kasner epoch, producing oscillatory Kasner exponents and an accumulation law tn∼ 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.
Related
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BibTeX
@misc{liu2026from,
title = {{From Critical Zero Modes to Interior Dynamics in Holographic Superconductors}},
author = {Yan Liu and Hong-Da Lyu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05208},
eprint = {2610.05208},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05208},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Critical Zero Modes to Interior Dynamics in Holographic Superconductors
AU - Yan Liu
AU - Hong-Da Lyu
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05208
UR - https://arxiv.org/abs/2610.05208
AB - 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_ER width and the phase Θ_J in the subsequent Josephson regime. If the condensate obeys t≡1−T/T_c∝ε^2r, then Δz_ER∝ t^1/r and Θ_J∝ t^−1/r. This Josephson phase is transferred to the first Kasner epoch, producing oscillatory Kasner exponents and an accumulation law t_n∼ 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.
ER -