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Creators/Authors contains: "Li, Warren"

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  1. Abstract We study the interior of black holes in the presence of charged scalar hair of small amplitude$$\epsilon $$ ϵ on the event horizon and show their terminal boundary is a crushing Kasner-like singularity. These spacetimes are spherically symmetric, spatially homogeneous and they differ significantly from the hairy black holes with uncharged matter previously studied in[M. Van de Moortel, Violent nonlinear collapse inside charged hairy black holes, Arch. Rational. Mech. Anal., 248, 89, 2024]in that the electric field is dynamical and subject to the backreaction of charged matter. We prove this charged backreaction causes drastically different dynamics compared to the uncharged case that ultimately impact the formation of the spacelike singularity, exhibiting novel phenomena such asCollapsed oscillations: oscillatory growth of the scalar hair, nonlinearly induced by the collapseAfluctuating collapse: The final Kasner exponents’ dependency in$$\epsilon $$ ϵ is via an expression of the form$$|\sin \left( \omega _0 \cdot \epsilon ^{-2}+ O(\log (\epsilon ^{-1}))\right) |$$ | sin ω 0 · ϵ - 2 + O ( log ( ϵ - 1 ) ) | .AKasner bounce: a transition from an unstable Kasner metric to a different stable Kasner metricThe Kasner bounce occurring in our spacetime is reminiscent of the celebrated BKL scenario in cosmology. We additionally propose a construction indicating the relevance of the above phenomena – including Kasner bounces – to spacelike singularities inside more general (asymptotically flat) black holes, beyond the hairy case. While our result applies to all values of$$\Lambda \in \mathbb {R}$$ Λ R , in the$$\Lambda <0$$ Λ < 0 case, our spacetime corresponds to the interior region of a charged asymptotically Anti-de-Sitter stationary black hole, also known as aholographic superconductorin high-energy physics, and whose exterior region was rigorously constructed in the recent mathematical work [W. Zheng,Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes, arXiv.2410.04758]. 
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