Kasner bounces and fluctuating collapse inside hairy black holes with charged matter

Abstract

We study the interior of black holes in the presence of charged scalar hair of small amplitude $\epsilon$ on the event horizon and show their terminal boundary is a crushing Kasner-like singularity. These spacetimes are 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. This charged backreaction causes drastically different dynamics compared to the uncharged case that impact the formation of the spacelike singularity, exhibiting novel phenomena such as - Collapsed oscillations: oscillatory growth of the scalar hair, nonlinearly induced by the collapse. - A fluctuating collapse: The final Kasner exponents' dependency in $\epsilon$ is via an expression of the form $|\sin \left({\omega }_0\cdot {\epsilon }^{-2}+O(\log ({\epsilon }^{-1}))\right)|$. - A Kasner bounce: a transition from an unstable Kasner metric to a different stable Kasner metric. The 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 $\Lambda \in \mathbb{R}$, in the $\Lambda <0$ case, our spacetime corresponds to the interior region of a charged asymptotically Anti-de-Sitter stationary black hole, also known as a holographic superconductor, 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].

arXiv commentSlight changes in the title and abstract. References updated. Final version, to appear in Annals of PDE

References in corpus (32)

• Building an AdS/CFT superconductor
• Holographic Superconductors
• Breaking an Abelian gauge symmetry near a black hole horizon
• Kerr black holes with scalar hair
• Stationary Black Holes: Uniqueness and Beyond
• Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields
• Introduction to Holographic Superconductors
• Quiescent cosmological singularities
• A proof of Price's law for the collapse of a self-gravitating scalar field
• The Bianchi IX attractor
• Black holes without spacelike singularities
• Smooth static solutions of the Einstein-Yang/Mills equation
• Diving into a holographic superconductor
• A scalar field condensation instability of rotating anti-de Sitter black holes
• Gravitational duals to the grand canonical ensemble abhor Cauchy horizons
• No Inner-Horizon Theorem for Black Holes with Charged Scalar Hairs
• Holographic flows from CFT to the Kasner universe
• Internal Structure of Einstein-Yang-Mills Black Holes
• Stable Big Bang formation for Einstein's equations: The complete sub-critical regime
• Mass inflation and chaotic behaviour inside hairy black holes
• A scattering theory for linear waves on the interior of Reissner-Nordström black holes
• Stability and instability of the sub-extremal Reissner-Nordström black hole interior for the Einstein-Maxwell-Klein-Gordon equations in spherical symmetry
• Diving inside a hairy black hole
• Mass inflation and the $C^2$-inextendibility of spherically symmetric charged scalar field dynamical black holes
• The maximal development of near-FLRW data for the Einstein-scalar field system with spatial topology ${\mathbb{S}}^3$
• The final Kasner regime inside black holes with scalar or vector hair
• AdS Black Holes with a Bouncing Interior
• Strong Cosmic Censorship in the presence of matter: the decisive effect of horizon oscillations on the black hole interior geometry
• Existence of exponentially growing finite energy solutions for the charged Klein-Gordon equation on the De Sitter-Kerr-Newman metric
• Polynomial Blow-up Upper Bounds for the Einstein-scalar field System Under Spherical Symmetry
• Extremal black holes that are not extremal: maximal warm holes
• New asymptotically (Anti)-de Sitter black holes in (super)gravity

Cited by in corpus (2)

• Exponentially-growing Mode Instability on Reissner-Nordström--Anti-de-Sitter black holes
• Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes