Pei-Ming HoHikaru KawaiHenry LiaoYuki Yokokura2024-10-292024-10-292024-07-18https://scholars.lib.ntu.edu.tw/handle/123456789/722585We study the interior metric of 4D spherically symmetric static black holes by using the semi-classical Einstein equation and find a consistent class of geometries with large curvatures. We approximate the matter fields by conformal fields and consider the contribution of the 4D Weyl anomaly, giving a state-independent constraint. Combining this with an equation of state yields an equation that determines the interior geometry completely. We explore the solution space of the equation in a non-perturbative manner for ħ. First, we find four types of asymptotic behaviors and examine the general features of the solutions. Then, by imposing physical conditions, we obtain approximately a general class of interior geometries: various combinations of dilute and dense structures without a horizon or singularity. This represents the diversity of the interior structure. Finally, we show that the number of possible patterns of such interior geometries corresponds to the Bekenstein–Hawking entropy.[SDGs]SDG11journal article10.1140/epjc/s10052-024-13058-0