Entropy emission properties of near-extremal Reissner-Nordstrm black holes

Bekenstein and Mayo have revealed an interesting property of evaporating (3 + 1)-dimensional Schwarzschild black holes: their entropy emission rates (S)over dot(Sch) are related to their energy emission rates P by the simple relation (S)over do>(Sch) = C-Sch x (P/h). (1/2), where CSch is a numerically computed dimensionless coefficient. Remembering that (1 + 1)-dimensional perfect black-body emitters are characterized by the same functional relation, (S)over dot(1+1) = C1+1 x (P/h)(1/2) [with C1+1 = (pi/3)(1/2)], Bekenstein and Mayo have concluded that, in their entropy emission properties, (3 + 1)-dimensional Schwarzschild black holes behave effectively as (1 + 1)-dimensional entropy emitters. Later studies have shown that this intriguing property is actually a generic feature of all radiating (D + 1)-dimensional Schwarzschild black holes. One naturally wonders whether all black holes behave as simple (1 + 1)-dimensional entropy emitters? In order to address this interesting question, we shall study in this paper the entropy emission properties of Reissner Nordstrom black holes. We shall show, in particular, that the physical properties which characterize the neutral sector of the Hawking emission spectra of these black holes can be studied analytically in the nearextremal T-BH -> 0 regime (here T-BH is the Bekenstein-Hawking temperature of the black hole). We find that the Hawking radiation spectra of massless neutral scalar fields and coupled electromagnetic-gravitational fields are characterized by the nontrivial entropy-energy relations (S)over dot(RN)(Scalar) = -C-RN(Scalar) x (AP(3)/h(3))(1/4) ln (AP/h) and (S)over dot(RN)(Elec-Grav) = -C(RN)(Elec-Grav)x(A(4)P(9)/h(9))(1/10) ln (AP/h) in the near-extremal T-BH -> 0 limit (here {C-RN(Scalar) , C-RN(Elec-Grav)} are analytically calculated dimensionless coefficients and A is the surface area of the Reissner-Nordstrom black hole). Our analytical results therefore indicate that not all black holes behave as simple (1 + 1)-dimensional entropy emitters.