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.

Physics of trans-Planckian gravity

“…Our results disagree with this point (see also [27] and note [33]). In fact, by conservation of energy, any experiment prepared at distance-scales smaller than the Planck length (and correspondingly energies bigger than the Planck energies) has to be surrounded by a classical BH.…”

Minimal Length Scale Scenarios for Quantum Gravity

“…In addition, towards the fixed point regime, the gravitational interaction becomes weaker, and with it weakening the argument from thought experiments in Section 3.1.2, which relied on the distortion caused by the gravitational attraction of the test particle. It has, in fact, been argued [51,108] that in ASG the formation of a black-hole horizon must not necessarily occur, and we recall that the formation of a horizon was the main spoiler for increasing the resolution in the earlier-discussed thought experiments.…”

Black holes within asymptotic safety

“…Further aspects of RG improved black hole geometries have been explored in Refs. [31,32,33,34,35]. 3 In general, these works established that quantum corrections in the vicinity of the nontrivial UV fixed points lead to drastic modifications of the classical picture at short distances or high momenta while the long-distance properties of the improved black hole spacetime essentially agree with classical general relativity.…”