Extremal critical collapse conjecture

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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 Ψ0∈M^non\Psi_0\in\widehat{\mathfrak M}_\mathrm{non} and Ψ1∈M^black\Psi_1\in\widehat{\mathfrak M}_\mathrm{black}; its critical parameter is p∗≐sup⁡{p∈[0,1]:Ψp∈M^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.

References

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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