It is often argued that the Planck length (or mass) is the scale of quantum gravity, as shown by comparing the Compton length with the gravitational radius of a particle. However, the Compton length is relevant in scattering processes but does not play a significant role in bound states. We will derive a possible ground state for a dust ball composed of a large number of quantum particles entailing a core with the size of a fraction of the horizon radius. This suggests that quantum gravity becomes physically relevant for systems with compactness of order one for which the nonlinearity of General Relativity cannot be discarded. A quantum corrected geometry can then be obtained from the effective energy-momentum tensor of the core or from quantum coherent states for the effective gravitational degrees of freedom. These descriptions replace the classical singularity of black holes with integrable structures in which tidal forces remain finite and there is no inner Cauchy horizon. The extension to rotating systems is briefly mentioned.

人们经常争论普朗克长度（或质量）是量子引力的尺度，通过将康普顿长度与粒子的引力半径进行比较来显示。然而，康普顿长度与散射过程相关，但在束缚态中起不重要作用。我们将推导出一个由大量量子粒子组成的尘球的可能基态，该尘球需要一个大小为水平半径的几分之一的核心。这表明量子引力与具有一阶紧凑性的系统在物理上相关，而广义相对论的非线性是不能丢弃的。然后，可以从核心的有效能量-动量张量或有效引力自由度的量子相干态获得量子校正几何。这些描述用可积结构取代了黑洞的经典奇点，其中潮汐力保持有限，并且没有内部柯西视界。简要提到了对旋转系统的扩展。