Classical limit for Dirac fermions with modified action in the presence of the black hole

Understand

We consider the model of Dirac fermions coupled to gravity as proposed in \cite{VolovikBH}, in which superluminal velocities of particles are admitted.

• In this model an extra term is added to the conventional Hamiltonian that originates from Planck physics.
• Due to this term a closed Fermi surface is formed in equilibrium inside the black hole.
• In this paper we propose the covariant formulation of this model and analyse its classical limit.