Asymptotic Safety, Asymptotic Darkness, and the hoop conjecture in the extreme UV

TL;DR

This paper explores how the formation of black holes in small-scale experiments is affected by asymptotically safe gravity, challenging the idea of a fundamental minimum length and showing that black hole formation depends on specific coupling values.

Contribution

It extends the hoop conjecture to include higher curvature terms within asymptotically safe gravity, analyzing black hole formation in the UV regime and its implications for minimum length arguments.

Findings

Black hole formation in small experiments depends on UV fixed point couplings.

No definitive proof that black holes always form in arbitrarily small regions.

Large horizons can form outside the experiment, preventing information escape.

Abstract

Assuming the hoop conjecture in classical general relativity and quantum mechanics, any observer who attempts to perform an experiment in an arbitrarily small region will be stymied by the formation of a black hole within the spatial domain of the experiment. This behavior is often invoked in arguments for a fundamental minimum length. Extending a proof of the hoop conjecture for spherical symmetry to include higher curvature terms we investigate this minimum length argument when the gravitational couplings run with energy in the manner predicted by asymptotically safe gravity. We show that argument for the mandatory formation of a black hole within the domain of an experiment fails. Neither is there a proof that a black hole doesn't form. Instead, whether or not an observer can perform measurements in arbitrarily small regions depends on the specific numerical values of the couplings near the UV fixed point. We further argue that when an experiment is localized on a scale much smaller than the Planck length, at least one enshrouding horizon must form outside the domain of the experiment. This implies that while an observer may still be able to perform local experiments, communicating any information out to infinity is prevented by a large horizon surrounding it, and thus compatibility with general relativity can still be restored in the infrared limit.