Dimensional dependence of critical phenomena in black hole interiors
Abstract
We numerically investigate the interior dynamics of D dimensional Reissner-Nordström (RN) black holes perturbed by a real scalar field. Strong perturbations destroy the null inner horizon and produce a spacelike singularity, whereas weaker perturbations preserve it with an areal radius that decreases as the perturbation amplitude increases. As the initial scalar field amplitude A approaches its critical value A*, the inner horizon radius decreases continuously to zero. Near criticality, this radius obeys the power law rs∝|A−A*|γ. In four dimensions, different initial scalar field profiles and initial RN black hole charges yield nearly identical critical exponents, γ≃1/2, supporting the universality of the scaling law. For 4≤ D≤9, the numerical results are well described by γ≃1/(D−2). The corresponding scaling, |A−A*|∝ rsD−2, indicates that the deviation of the initial parameter from its critical value is proportional to the area of the spherical cross section of the inner horizon.
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BibTeX
@misc{xin2026dimensional,
title = {{Dimensional dependence of critical phenomena in black hole interiors}},
author = {Li-Jie Xin and Xiangdong Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00829},
eprint = {2611.00829},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00829},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dimensional dependence of critical phenomena in black hole interiors
AU - Li-Jie Xin
AU - Xiangdong Zhang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00829
UR - https://arxiv.org/abs/2611.00829
AB - We numerically investigate the interior dynamics of D dimensional Reissner-Nordström (RN) black holes perturbed by a real scalar field. Strong perturbations destroy the null inner horizon and produce a spacelike singularity, whereas weaker perturbations preserve it with an areal radius that decreases as the perturbation amplitude increases. As the initial scalar field amplitude A approaches its critical value A^*, the inner horizon radius decreases continuously to zero. Near criticality, this radius obeys the power law r_s∝|A−A^*|^γ. In four dimensions, different initial scalar field profiles and initial RN black hole charges yield nearly identical critical exponents, γ≃1/2, supporting the universality of the scaling law. For 4≤ D≤9, the numerical results are well described by γ≃1/(D−2). The corresponding scaling, |A−A^*|∝ r_s^D−2, indicates that the deviation of the initial parameter from its critical value is proportional to the area of the spherical cross section of the inner horizon.
ER -