Quantum entropies in extreme dilaton black hole backgrounds

For spinor fields, the entropies from the spin-1/2- and spin-1/2(+) components, S-ext(q-) and S-ext(q+), are quite different, though the former is 7/8 times the scalar entropy and the latter contains an extra term. The brick wall model is applicable to both NEBH and EBH. For the EDBH with 0Pia(2)Pi1, using the brick wall model with the cutoff epsilon being given by epsilon((1-a2))/(1+a(2))=(1+a(2))kappam(2/(1+a2)) and kappa the surface gravity on the event horizon, at the Hawking temperature T-H=kappa/2pi, the scalar and spinor entropies are S-ext(q)=S-0/(1-a(2))(1+a(2))(2) with S-0=1/135 and S-Fext(q)=7/2 S-ext(q)+[1/6(1-a(2))], respectively. For the EGHSDBH, the spin-1/2(-) and spin 1/2(+) fields contribute the entropies S-ext(q-)= 7/8 S-ext(q), S-ext(q) =7/8S(ext)(q)+(pim/6beta) ln(L/epsilon), respectively; at the Hawking temperature, the spinor entropy is S-Fext(q)=(7/2+30)S-ext(q) with S-ext(q)=1/360 ln(L/epsilon).