标题： 近极端Reissner-Nordström黑洞的熵发射特性 显示英文标题

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

摘要： 贝肯施坦和梅奥揭示了蒸发的$(3+1)$-维史瓦西黑洞的一个有趣性质：它们的熵辐射率$\dot S_{\text{Sch}}$与其能量辐射率$P$之间存在简单的关系$\dot S_{\text{Sch}}=C_{\text{Sch}}\times (P/\hbar)^{1/2}$。 贝肯斯坦和梅奥注意到，$(1+1)$维完美黑体发射器具有相同的函数关系$\dot S^{1+1}=C^{1+1}\times(P/\hbar)^{1/2}$，他们得出结论，在熵发射特性方面，$(3+1)$维施瓦西黑洞在效果上表现为$(1+1)$维熵发射器。 人们自然会想知道，所有黑洞是否都表现为简单的$(1+1)$维熵发射器？ 为了探讨这个有趣的问题，本文将研究雷斯勒-诺德斯特姆黑洞的熵发射特性。 我们将特别展示，这些黑洞的霍金辐射谱中中性部分的物理特性可以在接近极端的$T_{\text{BH}}\to0$情况下{\it 分析上}进行研究。 我们发现，无质量中性标量场以及耦合的电磁-引力场的霍金辐射谱由非平凡的能量-熵关系$\dot S^{\text{Scalar}}_{\text{RN}} = -C^{\text{Scalar}}_{\text{RN}} \times (AP^3/\hbar^3)^{1/4} \ln(AP/\hbar)$和$\dot S^{\text{Elec-Grav}}_{\text{RN}} = -C^{\text{Elec-Grav}}_{\text{RN}} \times (A^4P^9/\hbar^9)^{1/10} \ln(AP/\hbar)$在近极端$T_{\text{BH}}\to0$极限下刻画（这里$A$是 Reissner-Nordström 黑洞的表面积）。 因此，我们的解析结果表明，{\it 不是}所有黑洞的行为都类似于简单的$(1+1)$维熵发射器。 显示英文摘要

摘要： 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 $\dot S_{\text{Sch}}=C_{\text{Sch}}\times (P/\hbar)^{1/2}$. Remembering that $(1+1)$-dimensional perfect black-body emitters are characterized by the same functional relation, $\dot S^{1+1}=C^{1+1}\times(P/\hbar)^{1/2}$, 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-Nordstr\"om 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 $T_{\text{BH}}\to0$ 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 $\dot S^{\text{Scalar}}_{\text{RN}} = -C^{\text{Scalar}}_{\text{RN}} \times (AP^3/\hbar^3)^{1/4} \ln(AP/\hbar)$ and $\dot S^{\text{Elec-Grav}}_{\text{RN}} = -C^{\text{Elec-Grav}}_{\text{RN}} \times (A^4P^9/\hbar^9)^{1/10} \ln(AP/\hbar)$ in the near-extremal $T_{\text{BH}}\to0$ limit (here $A$ is the surface area of the Reissner-Nordstr\"om black hole). Our analytical results therefore indicate that {\it not} all black holes behave as simple $(1+1)$-dimensional entropy emitters.