  One quantum characterization of a black hole motivated by (local) holography
and thermodynamics is that it maximizes thermodynamic entropy for a given
surface area. In the context of quantum gravity, this could be more fundamental
than the classical characterization by a horizon. As a step, we explore this
possibility by solving the 4D semi-classical Einstein equation with many matter
fields, and find a picture of a black hole. For spherical static highly-excited
configurations, we apply local typicality and estimate the entropy including
self-gravity to derive its upper bound. The saturation condition uniquely
determines the entropy-maximized configuration: self-gravitating quanta
condensate into a radially-uniform dense configuration with no horizon, where
the self-gravity and a large quantum pressure induced by the curvatures are
balanced and no singularity appears. The interior metric is a self-consistent
and non-perturbative solution for Planck's constant. The maximum entropy, given
by the volume integral of the entropy density, agrees with the
Bekenstein-Hawking formula through self-gravity, deriving the Bousso bound for
thermodynamic entropy. Finally, 10 future prospects are discussed, leading to
the speculative view that the configuration represents semi-classically a
quantum-gravitational condensate with holographic bulk dynamics.
