The entropy emission properties of near-extremal Reissner-Nordström black holes

Abstract

Bekenstein and Mayo have revealed an interesting property of evaporating $(3+1)$-dimensional Schwarzschild black holes: their entropy emission rates ${\dot{S}}_{\text{Sch}}$ are related to their energy emission rates $P$ by the simple relation ${\dot{S}}_{\text{Sch}}=C_{\text{Sch}}\times (P/\hslash {)}^{1/2}$. Remembering that $(1+1)$-dimensional perfect black-body emitters are characterized by the same functional relation, ${\dot{S}}^{1+1}=C^{1+1}\times (P/\hslash {)}^{1/2}$, 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. 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-Nordström 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 {\it analytically} in the near-extremal $T_{\text{BH}}\to 0$ regime. We find that the Hawking radiation spectra of massless neutral scalar fields and coupled electromagnetic-gravitational fields are characterized by the non-trivial entropy-energy relations ${\dot{S}}_{\text{RN}}^{\text{Scalar}}=-C_{\text{RN}}^{\text{Scalar}}\times (A{P}^3/{\hslash }^3{)}^{1/4}\ln (AP/\hslash )$ and ${\dot{S}}_{\text{RN}}^{\text{Elec-Grav}}=-C_{\text{RN}}^{\text{Elec-Grav}}\times (A^4{P}^9/{\hslash }^9{)}^{1/10}\ln (AP/\hslash )$ in the near-extremal $T_{\text{BH}}\to 0$ limit (here $A$ is the surface area of the Reissner-Nordström black hole). Our analytical results therefore indicate that {\it not} all black holes behave as simple $(1+1)$-dimensional entropy emitters.

5 pages

References in corpus (2)

• Low-frequency absorption cross section of the electromagnetic waves for the extreme Reissner-Nordstrom black holes in higher dimensions
• Ten shades of black

Cited by in corpus (6)

• Decoding infrared imprints of quantum origins of black holes
• Maximum rate of entropy emission
• A note on entropy of matter in presence of gravity: status of extensivity of entropy
• The Hawking paradox and the Bekenstein resolution in higher-dimensional spacetimes
• Natural broadening in the quantum emission spectra of higher-dimensional Schwarzschild black holes
• Black hole entropy emission property