Critical phenomenon inside asymptotically flat black holes with spontaneous scalarization

TL;DR

This paper investigates the internal structure of spontaneously scalarized black holes, revealing critical phenomena where the inner horizon becomes a spacelike singularity and establishing a scaling relation near bifurcation points.

Contribution

It uncovers the critical behavior and singularity formation inside scalarized black holes, providing new insights into their interior dynamics and bifurcation properties.

Findings

Scalarized black holes lack smooth inner horizons and develop Kasner singularities.

A scaling relation links the Kasner parameter to the charge-to-mass ratio near bifurcation.

Rapid collapse of the Einstein-Rosen bridge occurs at the would-be Cauchy horizon.

Abstract

We study the 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-Nordstrom solution, we establish a robust scaling relation between the Kasner parameter and the charge-to-mass ratio of the hairy black hole, opening a new window into the remarkable simplicity underlying black hole interiors.