The black hole final state for the Dirac fields In Schwarzschild spacetime

TL;DR

This paper demonstrates that the black hole final state for massless Dirac fields can be modeled as an entangled state of matter and radiation, supporting the Horowitz-Maldacena conjecture for fermionic fields and showing mixedness decreases during evaporation.

Contribution

It extends the black hole final state proposal to fermionic fields, showing the applicability of the Horowitz-Maldacena conjecture to Dirac fields in Schwarzschild spacetime.

Findings

Black hole internal state for Dirac fields is entangled

Horowitz-Maldacena conjecture applies to fermionic fields

Mixedness decreases during black hole evaporation

Abstract

We show that the internal stationary state of a black hole for massless Dirac fields can be represented by an entangled state of collapsing matter and infalling Hawking radiation. This implies that the Horowitz-Maldacena conjecture for the black hole final state originally proposed for the massless scalar fields is also applicable to fermionic fields as well. For an initially mixed state we find that the measure of mixedness is expected to decrease under evaporation.