Entropy of the Dirac field in a Kerr-Newman black hole

Thinking of the Dirac equations in Newman-Penrose formalism, there are four components of the wave function ψ₁₁,ψ₁₂,ψ₂₁,ψ₂₂. We consider that the total free energy is summed up from the free energies of the four components. Then the entropy of the Dirac field in a Kerr-Newman black hole is calculated via the brick-wall method. We find that the calculation of the Dirac field is similar to that of a scalar field. It also requires a radial and an angular cutoff {ε} and {δ}. Moreover, if the cutoff values ε and {δ} satisfy the same proper relation in the scalar field between them, the resulting entropy is 7/2 times the Klein-Gordon field.