Fermion condensate at the event horizon

TL;DR

The paper explores how modifying fermionic anticommutation relations near a black hole's event horizon can lead to a fermion condensate, using an ad hoc source in the Dirac equation to model this effect.

Contribution

It introduces a novel approach to model fermion behavior near black hole horizons by modifying the Dirac equation with an ad hoc source, resulting in stationary Green's functions.

Findings

Stationary Green's functions indicate a fermion condensate near the event horizon.

Modification of anticommutation relations affects the source term in the Dirac equation.

The approach provides a new perspective on fermionic quantum states in curved spacetime.

Abstract

Some arguments are considered in favor of the idea that the canonical anticommutation relations for fermions should be modified in curved spacetime near the event horizon of a black hole. Such a modification is expected to lead to a change in the source term of the inhomogeneous Dirac equation describing the two-point Green's function. By introducing an {\it ad hoc} source into the Dirac equation that mimics the modification of these anticommutation relations, stationary solutions are obtained and interpreted as two-point Green's functions of fermions located near the event horizon. Owing to their stationarity, these Green's functions describe a fermion condensate near the event horizon.