Quantum kinetic theory of a massless scalar model in the presence of a Schwarzschild black hole

Abstract: 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.