Emergent Scaling Symmetry and Universal Interior Criticality of Scalarized Black Holes
Abstract
The interiors of spontaneously scalarized charged black holes exhibit a tower of universality classes, including the previously reported 1/2 scaling. We show that their near-critical collapse is governed by an emergent scaling symmetry at the would-be Cauchy horizon. This symmetry renders the interior dynamics autonomous, model-independent, and exactly integrable, realizing first-kind self-similarity rather than Choptuik-type second-kind criticality. It also yields a ``seesaw amplification'': an arbitrarily small exterior hair produces an arbitrarily large interior response. The amplification obeys an amplitude identity relating three independently measurable quantities. The singularity exponent equals the critical exponent of the exterior scalar charge. These relations connect the exterior phase transition to the approach to the interior singularity through the scaling dynamics near the would-be Cauchy horizon.
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BibTeX
@misc{sun2026emergent,
title = {{Emergent Scaling Symmetry and Universal Interior Criticality of Scalarized Black Holes}},
author = {Ze Sun and Fu-Guo Yang and Rong-Gen Cai and Li Li and Run-Qiu Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.30240},
eprint = {2609.30240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30240},
}
RIS
TY - UNPB
TI - Emergent Scaling Symmetry and Universal Interior Criticality of Scalarized Black Holes
AU - Ze Sun
AU - Fu-Guo Yang
AU - Rong-Gen Cai
AU - Li Li
AU - Run-Qiu Yang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2609.30240
UR - https://arxiv.org/abs/2609.30240
AB - The interiors of spontaneously scalarized charged black holes exhibit a tower of universality classes, including the previously reported 1/2 scaling. We show that their near-critical collapse is governed by an emergent scaling symmetry at the would-be Cauchy horizon. This symmetry renders the interior dynamics autonomous, model-independent, and exactly integrable, realizing first-kind self-similarity rather than Choptuik-type second-kind criticality. It also yields a ``seesaw amplification'': an arbitrarily small exterior hair produces an arbitrarily large interior response. The amplification obeys an amplitude identity relating three independently measurable quantities. The singularity exponent equals the critical exponent of the exterior scalar charge. These relations connect the exterior phase transition to the approach to the interior singularity through the scaling dynamics near the would-be Cauchy horizon.
ER -