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 $\mathrm{\Delta }p\equiv p-p^{⁎}$ 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.

中文翻译：

---

Choptuik临界指数的一个猜想上限

接近临界的II型重力塌陷的特征是形成了任意小的黑洞，其黑洞半径由简单的比例定律描述。 ${\mathrm{[R}}_{\text{BH}}\propto {（p-p^{⁎}）}^{\gamma }$，其中γ是与物质有关的Choptuik临界指数，而$\mathrm{\Delta }p\equiv p-p^{⁎}$是距精确的自相似临界演化的相空间距离。我们指出，到目前为止，物理学文献中研究的所有物质模型都具有上限$\gamma \le \mathrm{1个}$。我们推测这是非线性重力坍塌情况的普遍特征。