Extremal critical collapse conjecture

From papers

Let M^\widehat{\mathfrak M} be a moduli space of Cauchy data on R3\mathbb R^3 for a matter-model and symmetry-class combination in which an exact extremal Kerr--Newman event horizon can form in finite time. An interpolating family is a continuous family {Ψp}p[0,1]M^\{\Psi_p\}_{p\in[0,1]}\subset\widehat{\mathfrak M} with Ψ0M^non\Psi_0\in\widehat{\mathfrak M}_\mathrm{non} and Ψ1M^black\Psi_1\in\widehat{\mathfrak M}_\mathrm{black}; its critical parameter is psup{p[0,1]:ΨpM^non}p_*\doteq\sup\{p\in[0,1]:\Psi_p\in\widehat{\mathfrak M}_\mathrm{non}\}. Extremal critical collapse conjecture. There exist data producing an exactly extremal Kerr--Newman event horizon after a stationary subextremal apparent horizon, with the event horizon absent from the initial Cauchy hypersurface; there exist interpolating families whose critical solution forms an asymptotically extremal Kerr--Newman black hole; near such a critical solution, the threshold has the stated Kerr--Newman structure, scaling laws, and horizon instabilities. This conjecture was disproved according to the supplied status evidence.

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Sources & referencesView supporting material

Primary source

Yannis Angelopoulos, Christoph Kehle and Ryan Unger, “The moduli space of dynamical spherically symmetric black hole spacetimes and the extremal threshold”, arXiv:2603.10378 (2026).

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