Li Li

Spontaneous scalarization of charged black holes in asymptotically flat spacetime has attracted much recent interest. It is recently reported that inside these spontaneously scalarized black holes, the Kasner parameter $β$ at the terminal singularity diverges as $β\propto(q/q_c-1)^{-γ}$ near the critical charge-to-mass ratio $q_c$, with an exponent $γ=1/2$ that appeared model independent within a wide class of couplings. In this paper we report a family of new universality classes in which $γ$ differs from 1/2. We show that all these critical behaviors are governed by the same emergent scaling symmetry at the would-be Cauchy horizon of the background Reissner-Nordström solution. This symmetry leads to a ``seesaw amplification'' to amplify exterior small scalar and produces a limiting autonomous system that is independent of the details of the theory. Our mechanism provides a unified picture of exterior scalarization and interior criticality and makes sharp numerical predictions that we test.