  We employ quantum kinetic theory to investigate local quantum physics in the
background of spherically symmetric and neutral black holes formed through the
gravitational collapse. For this purpose in mind, we derive and study the
covariant Wigner distribution function $\mathcal{W}(x,p)$ near to and far away
from the black-hole horizon. We find that the local density of the particle
number is negative in the near-horizon region, while the entropy density is
imaginary. These pose a question whether kinetic theory is applicable in the
near-horizon region. We elaborate on that and propose a possible interpretation
of how this result might nevertheless be self-consistently understood.
