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

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.

arXiv comment9 pages, Matched Published Version with minor changes for clarity and emphasis of key points

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• Scale Setting for Self-consistent Backgrounds
• Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
• Asymptotically Safe gravity and non-singular inflationary Big Bang with vacuum birth
• Cosmological constant problem: deflation during inflation
• More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons
• Can we see quantum gravity? Photons in the asymptotic-safety scenario
• Deformed Special Relativity from Asymptotically Safe Gravity
• How not to establish the non-renormalizability of gravity
• Black holes in asymptotic safety with higher derivatives: accretion and stability analysis
• Singularities and Phenomenological aspects of Asymptotic Safe Gravity