Violent Nonlinear Collapse in the Interior of Charged Hairy Black Holes

We construct a new one-parameter family, indexed by ε ϵ , of two-ended, spatially-homogeneous black hole interiors solving the Einstein–Maxwell–Klein–Gordon equations with a (possibly zero) cosmological constant Λ Λ and bifurcating off a Reissner–Nordström-(dS/AdS) interior ( ε =0 ϵ = 0 ). For all small ε ≠ 0 ϵ ≠ 0 , we prove that, although the black hole is charged, its terminal boundary is an everywhere- spacelike Kasner singularity foliated by spheres of zero radius r . Moreover, smaller perturbations (i.e. smaller |ε | | ϵ | ) are more singular than larger ones , in the sense that the Hawking mass and the curvature blow up following a power law of the form r^-O(ε ⁻²) r - O ( ϵ - 2 ) at the singularity =0\ { r = 0 } . This unusual property originates from a dynamical phenomenon— violent nonlinear collapse —caused by the almost formation of a Cauchy horizon to the past of the spacelike singularity =0\ { r = 0 } . This phenomenon was previously described numerically in the physics literature and referred to as “the collapse of the Einstein–Rosen bridge”. While we cover all values of Λ ∈ R Λ ∈ R , the case Λ <0 Λ < 0 is of particular significance to the AdS/CFT correspondence. Our result can also be viewed in general as a first step towards the understanding of the interior of hairy black holes.