https://doi.org/10.1140/epjc/s10052-024-13058-0
Regular Article - Theoretical Physics
4D Weyl anomaly and diversity of the interior structure of quantum black hole
1
Department of Physics and Center for Theoretical Physics, National Taiwan University, 106, Taipei, Taiwan
2
Physics Division, National Center for Theoretical Sciences, 10617, Taipei, Taiwan
3
iTHEMS Program, RIKEN, 351-0198, Wako, Saitama, Japan
Received:
28
April
2024
Accepted:
26
June
2024
Published online:
18
July
2024
We 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 
. 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.
© The Author(s) 2024
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