Kasner critical scaling in Einstein--Maxwell--scalar black holes with nonlinear collapse and scalarization
Year: 2026
Type: preprint
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 $m\ge1$ by tuning higher-order terms at fixed quadratic coupling parameter $μ$. Nonlinear interior collapse produces a spacelike Kasner singularity with $β_{\rm K}\propto\varepsilon^{-1}$, where $\varepsilon$ is the value of scalar field at the event horizon. An exterior branch satisfying $q/q_\star-1\propto\varepsilon^{2m}$, therefore, yields $β_{\rm K}\propto|q/q_\star-1|^{-1/(2m)}$, where $q$ is the charge-to-mass ratio and $q_\star$ its critical value. We also determine the prefactor explicitly. This recovers the $1/2$ law and establishes a hierarchy including $1/4$ and $1/6$.
Source: arXiv (Cornell University)
Authors: He, Chihang, Liu, Chao
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G5836243928, G7105993024
OpenAlex ID: W7214777898