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Kasner critical scaling in Einstein--Maxwell--scalar black holes with nonlinear collapse and scalarization

  • Chihang He
  • Chao Liu
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Abstract

A critical scaling exponent of 1/2 was numerically observed for the Kasner parameter of asymptotically flat scalarized black holes and conjectured to be universal [Phys.\ Rev.\ Lett.\ \textbf{136}, 251402 (2026)]. In the same static, spherically symmetric Einstein--Maxwell--scalar setting, we show that this exponent is not universal. We develop a rigorous mathematical framework and construct couplings realizing exponents 1/(2m) for any integer m≥1 by tuning higher-order terms at fixed quadratic coupling parameter μ. Nonlinear interior collapse produces a spacelike Kasner singularity with βK∝ε−1, where ε is the value of scalar field at the event horizon. An exterior branch satisfying q/q⋆−1∝ε2m, therefore, yields βK∝|q/q⋆−1|−1/(2m), where q is the charge-to-mass ratio and q⋆ its critical value. We also determine the prefactor explicitly. This recovers the 1/2 law and establishes a hierarchy including 1/4 and 1/6.

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Cite

BibTeXRIS
BibTeX
@misc{he2026kasner,
  title = {{Kasner critical scaling in Einstein--Maxwell--scalar black holes with nonlinear collapse and scalarization}},
  author = {Chihang He and Chao Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35500},
  eprint = {2609.35500},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35500},
}
RIS
TY  - UNPB
TI  - Kasner critical scaling in Einstein--Maxwell--scalar black holes with nonlinear collapse and scalarization
AU  - Chihang He
AU  - Chao Liu
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35500
UR  - https://arxiv.org/abs/2609.35500
AB  - A critical scaling exponent of 1/2 was numerically observed for the Kasner parameter of asymptotically flat scalarized black holes and conjectured to be universal [Phys.\ Rev.\ Lett.\ \textbf{136}, 251402 (2026)]. In the same static, spherically symmetric Einstein--Maxwell--scalar setting, we show that this exponent is not universal. We develop a rigorous mathematical framework and construct couplings realizing exponents 1/(2m) for any integer m≥1 by tuning higher-order terms at fixed quadratic coupling parameter μ. Nonlinear interior collapse produces a spacelike Kasner singularity with β_K∝ε^−1, where ε is the value of scalar field at the event horizon. An exterior branch satisfying q/q_⋆−1∝ε^2m, therefore, yields β_K∝|q/q_⋆−1|^−1/(2m), where q is the charge-to-mass ratio and q_⋆ its critical value. We also determine the prefactor explicitly. This recovers the 1/2 law and establishes a hierarchy including 1/4 and 1/6.
ER  -