Violent Nonlinear Collapse in the Interior of Charged Hairy Black Holes

Abstract We construct a new one-parameter family, indexed by ϵ, of two-ended, spatially-homogeneous black hole interiors solving the Einstein–Maxwell–Klein–Gordon equations with a (possibly zero) cosmological constant Λ and bifurcating off a Reissner–Nordström- (dS/AdS) interior (=0 ϵ = 0). For all small 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 |) 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 (^{-2) } r - O (ϵ - 2) at the singularity \r=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 \r=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 R Λ ∈ R, the case 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.