Kasner Critical Scaling in Einstein-Maxwell-scalar Black Holes with Nonlinear Collapse and Scalarization
Time: 2026-10-30
Published By: He Liu
Speaker(s): Chao Liu (Huazhong University of Science and Technology)
Time: 16:00-17:00 November 9, 2026
Venue: Room 78301, Jingchunyuan 78, BICMR
We rigorously establish critical scaling laws linking the exterior charge-to-mass ratio $q$ to the terminal Kasner parameter $\beta_{\mathrm K}$ of static, spherically symmetric, asymptotically flat Einstein--Maxwell--scalar black holes. A critical 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)]. We disprove this conjecture in the same static, spherically symmetric Einstein--Maxwell--scalar setting. Under suitable coupling assumptions, we rigorously construct scalarized branches realizing exponents $1/(2m)$ for any integer $m\ge1$ by tuning higher-order coupling terms at fixed quadratic coupling parameter $\mu$. The interior evolution terminates at a spacelike Kasner singularity with $\beta_{\rm K}\sim(\lambda_I/\iota)\varepsilon^{-1}$ as $\varepsilon\to0^+$, where $\varepsilon$ is the scalar field at the event horizon, while the exterior branch satisfies $q/q_{\star}-1\sim c_{2m}\varepsilon^{2m}$, with $c_{2m}\ne0$. Consequently, \begin{equation*} \beta_{\rm K}\sim \frac{\lambda_I}{\iota}|c_{2m}|^{1/(2m)} \left|\frac{q}{q_{\star}}-1\right|^{-1/(2m)}, \end{equation*} where $\lambda_I/\iota=\pi/\cosh\!\left(\pi\sqrt{\mu-\tfrac14}\right)$. Thus the $1/2$ law is the nondegenerate $m=1$ case, while suitable higher-order tuning yields a hierarchy including $1/4$ and $1/6$.
