A black hole is considered as a bound state consisting of many semi-classical degrees of freedom responsible for the entropy which exist uniformly inside and have maximum gravity. The distribution of their information determines the interior metric through the semi-classical Einstein equation. Then, the interior is a continuous stacking of $AdS_2\times S^2$ without horizon or singularity and behaves like a local thermal state at a near-Plankian local temperature. Evaluating the entropy density from thermodynamic relations and integrating it over the interior volume, the area law is obtained with the factor 1/4 for any interior degrees of freedom, where the dynamics of gravity plays an essential role in changing the entropy from the volume law to the area law. [arXiv: 2207.14274]
Nobuyuki Matsumoto