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arXiv · 2604.00204

No-Go Theorem for Singularity Resolution

Zhen-Xiao Zhang·Chen Lan·Yan-Gang Miao
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Abstract

We prove a No-Go theorem for singularity resolution in homogeneous, spatially flat gravitational collapse: within this sector, quantum corrections introduced solely as non-vanishing effective matter sources are insufficient to halt singularities in any vacuum-normalized analytic gravitational theory, including general relativity and other theories with analytic gravitational actions. This theorem rules out singularity resolution via effective energy density in a broad class of quantum gravity approaches, including asymptotic safety and noncommutative geometry theories, where the effective energy densities yield finite-time singularities or geodesic incompleteness. The singularity resolution strictly requires non-analytic modifications of the gravitational response at $\mathbb{Q}=0$, or a vanishing effective energy density at high densities (as realized in loop quantum gravity's Planck stars). The theorem is proved via an intrinsic $f(\mathbb{Q})$ gravity framework, extended universally to general relativity, $f(\mathbb{R})$, and $f(\mathbb{T})$ theories through the geometrical trinity at the level of the corresponding homogeneous collapse response structure--with regularity criteria and junction conditions grounded in non-metricity, free of standard GR tools.

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Zhen-Xiao Zhang, Chen Lan, Yan-Gang Miao. 2026-03-31. No-Go Theorem for Singularity Resolution. https://arxiv.org/abs/2604.00204

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