A conjectured upper bound on the Choptuik critical exponents

Near-critical type II gravitational collapse is characterized by the formation of arbitrarily small black holes whose horizon radii are described by the simple scaling law r(BH) alpha (p - p*)(gamma), where gamma is the matter-dependent Choptuik critical exponent and Delta p p - p* is the phase space distance from the exact self-similar critical evolution. We point out that all matter models studied thus far in the physics literature are characterized by the upper bound gamma <= 1. We conjecture that this is a generic feature of non-linear gravitational collapse scenarios. (C) 2021 The Author(s). Published by Elsevier B.V.