Fermion emission in a two-dimensional black hole space-time

TL;DR

This paper studies how massless fermions are emitted by a two-dimensional dilatonic black hole, revealing the thermal nature of the radiation near the horizon through Bogoliubov transformations.

Contribution

It provides a detailed analysis of fermion emission using Bogoliubov transformations, accounting for non-invertibility and non-unitarity, and characterizes the thermal nature of the radiation.

Findings

Fermion emission exhibits thermal characteristics near the horizon.

The particle content is described by inclusive probabilities for outgoing fermions.

The analysis accounts for the non-invertibility of the Bogoliubov transformation.

Abstract

We investigate massless fermion production by a two-dimensional dilatonic black hole. Our analysis is based on the Bogoliubov transformation relating the outgoing fermion field observed outside the black hole horizon to the incoming field present before the black hole creation. It takes full account of the fact that the transformation is neither invertible nor unitarily implementable. The particle content of the outgoing radiation is specified by means of inclusive probabilities for the detection of sets of outgoing fermions and antifermions in given states. For states localized near the horizon these probabilities characterize a thermal equilibrium state. The way the probabilities become thermal as one approaches the horizon is discussed in detail.