Abstract
AbstractWe 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 $$\hbar $$
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.
Publisher
Springer Science and Business Media LLC
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