Critical Kasner scaling from Cauchy-horizon collapse near holographic phase transitions
Abstract
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∝|λ−λc|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-AdS4 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.
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BibTeX
@misc{gao2026critical,
title = {{Critical Kasner scaling from Cauchy-horizon collapse near holographic phase transitions}},
author = {Ling-Long Gao and Yan Liu and Hong-Da Lyu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24227},
eprint = {2609.24227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24227},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Critical Kasner scaling from Cauchy-horizon collapse near holographic phase transitions
AU - Ling-Long Gao
AU - Yan Liu
AU - Hong-Da Lyu
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24227
UR - https://arxiv.org/abs/2609.24227
AB - 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∝|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.
ER -