We study a spherical black hole formed slowly in a heat bath in the context of ordinary field theory, which we expect to have the typical properties of black holes.
We assume that the matter field is conformal and that the metric satisfies the semi-classical Einstein equation. Then, as a necessary condition, its trace part must be satisfied, which is determined only by the metric through the 4-dimensional Weyl anomaly independently of the quantum state. With some physically reasonable assumptions, this equation restricts the interior metric to a certain class.
Such metrics are approximately warped products of AdS_2 and S^2 with almost Planckian curvature.
Among them, we find one that is consistent with Hawking radiation and is smoothly connected to the exterior Schwarzschild metric slightly outside the Schwarzschild radius.
This leads to a picture that the black hole is a dense object with a surface (not a horizon), which evaporates due to Hawking-like radiation when taken out of the bath.
[arXiv: 2108.02242]