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

## TL;DR

This paper uses quantum kinetic theory to analyze particle behavior near black holes, revealing unusual negative densities and imaginary entropy densities close to the horizon, raising questions about the theory's applicability in such extreme regions.

## Contribution

It derives the covariant Wigner distribution function in black hole backgrounds and explores its implications near the horizon, highlighting potential limitations of kinetic theory in these conditions.

## Key findings

- Negative local particle density near the horizon
- Imaginary entropy density close to the horizon
- Discussion on the applicability of kinetic theory in extreme gravitational fields

## 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.