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arXiv · 2608.19581

Optimal Extension Regularity at the McVittie Event Horizon

Yi-kun Li
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Abstract

We determine the optimal local extension regularity of the future black-hole event horizon in the exact spatially flat McVittie solutions sourced by a positive cosmological constant and a barotropic fluid with constant equation-of-state parameter $w>-1$. Let $H_\infty$ be the asymptotic Hubble constant, $\kappa$ the surface gravity of the limiting black-hole root, and $p=3(1+w)H_\infty/\kappa$. Ingoing radial null geodesics reach the horizon in finite affine length. A parallelly propagated angular curvature component is asymptotic to $C s^{p-2}$, with $C\ne0$ and $s$ the remaining affine distance, which excludes every anchored $C^2$ extension for $0 \vartheta$. Every integer $p\ge2$ instead belongs to an analytic island and admits a real-analytic local extension. At the critical value $p=2$ the boundary Einstein endomorphism has a nonzero rank-one nilpotent part. The ratio of cosmological decay to horizon redshift therefore determines a sharp, arithmetic hierarchy of geometric regularity.

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Yi-kun Li. 2026-08-20. Optimal Extension Regularity at the McVittie Event Horizon. https://arxiv.org/abs/2608.19581

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