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 $r_{\text{BH}}\propto {(p-p^{⁎})}^{\gamma }$, where γ is the matter-dependent Choptuik critical exponent and $\Delta p\equiv p-p^{⁎}$ 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 $\gamma \le 1$. We conjecture that this is a generic feature of non-linear gravitational collapse scenarios.