Entanglement entropy for a Dirac field in a black shell

A quantum field of s = 1/2 in the vicinity of a dust shell contracting at a distance r(t0) to near its gravitational radius rs as seen by a FIDO observer is considered. Such an observer perceives a batch of particles around the event horizon. The origin of the particles around the spherical surface of radius r = rs + epsilon lies in the thermal excitations in the Boulware vacuum state, I0)B for an external observer. The foregoing is done based on thermo field dynamics, as it allows one to explain the origin of SBH as a state of entanglement between the modes of the fermionic field spreading through the Kruskal variety SEnt proportional to SBH with respect to a FIDO observer. A location of the degrees of freedom responsible for SBH entropy is given. The occupation number for particles of a half-integer spin s = 1/2 is estimated, and it is compared with the occupation number of particles of spin s = 0, finding that the occupation number of the Dirac field is slightly lower than the occupation number of scalar particles in the vicinity of the gravitational radius; this allows confirming the exclusion principle near event horizons. The other thermodynamic properties of the field are estimated.