Black Shells, Dirac's Field and the species problem

TL;DR

This paper models the thermal atmosphere around a black hole as vacuum excitations near a collapsing shell, proposing a solution to the species problem by relating entropy to entanglement entropy, independent of field types.

Contribution

It introduces a thermodynamic model of a fermionic field near a black hole's horizon and offers a novel resolution to the species problem by linking entropy to entanglement entropy.

Findings

Entropy is derived as entanglement entropy of the thermal atmosphere.

The species problem is addressed by showing entropy independence from the number of fields.

A natural cutoff is justified through shell equations of motion.

Abstract

We describe a thermal atmosphere around a black hole as vacuum excitations near to gravitational radius of a contracting thin black shell, i.e., in terms of properties of the physical vacuum of fields around a thin shell of mass $M$ collapsing from infinity to the Schwarzschild radius according to an external stationary observer. A natural explanation is introduced for the necessary cutoff using the equations of motion of the shells. We make a thermodynamic description of a fermionic field near the gravitational radius. Then a solution to the species problem for two fields, scalar one and spinor one, is proposed. Finally we get the Bekenstein-Hawking entropy as entanglement entropy of a thermal atmosphere, independent from number of fields.