Critical Phenomenon inside Asymptotically Flat Black Holes with Spontaneous Scalarization
Phys. Rev. Lett. 136, 251402 – Published 23 June, 2026
DOI: https://doi.org/10.1103/l4tf-kqyl
Abstract
We study the nonlinear interior dynamics of spontaneously scalarized black holes in Einstein-Maxwell-scalar theory with zero cosmological constant, revealing novel critical phenomena. We demonstrate that, for a wide range of scalar-electromagnetic couplings, scalarized black holes possess no smooth inner Cauchy horizon and instead evolve into a spacelike Kasner singularity. The scalar hair triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Near the critical point where scalarized black holes bifurcate from the Reissner-Nordström solution, we establish a robust scaling relation between the Kasner exponent and the charge-to-mass ratio of the hairy black hole, opening a new window into the remarkable simplicity underlying black hole interiors.
