  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 $G_{\mu\nu}=8\pi G \langle \psi|
T_{\mu\nu}|\psi \rangle$, where $|\psi \rangle$ is the wave function of the
matter field. Then as a necessary condition, its trace part must be satisfied,
$G^\mu{}_\mu=8\pi G \langle \psi| T^\mu{}_\mu|\psi \rangle$, whose right-hand
side is independent of $|\psi \rangle$ and is determined only by the metric
through the 4-dimensional Weyl anomaly. 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. Other solutions
represent objects that are larger in size than a black hole, which may be
useful for analyzing ultra-dense stars.
