标题： 弦理论中的霍金辐射和黑洞的弦相 显示英文标题

标题： Hawking Radiation in String Theory and the String Phase of Black Holes

摘要： 黑洞通过量子弦发射是在“弦类比模型”（或热力学方法）框架中计算的，该模型非常适合在弯曲背景（特别是这里，黑洞和弦具有内在的热特性及温度）中结合场论和弦理论。 QFT-霍金温度 T_H 在黑洞背景下受到弦温度 T_S 的上限限制。 黑洞发射谱是 (T_H - T_S) 的不完全伽马函数。 当 T_H << T_S 时，它产生 QFT-霍金辐射。 当 T_H\to T_S 时，它显示出高度质量的弦态主导发射，并经历典型的弦相变，转变为质量为 M_{\min }或半径为 r_{\min }的微观“最小”黑洞（与 T_S 成反比）和弦温度 T_S。 半经典 QFT 黑洞（质量为 M 和温度为 T_H）和弦黑洞（质量为 M_{最小值}和温度为 T_S）通过“对偶”变换相互映射，该变换连接了经典/QFT 和量子弦区域。 弦的反作用效应（半经典爱因斯坦方程的自洽黑洞解，质量为 M_+（半径为 r_+）和温度为 T_+）被计算出来。 两者，QFT 和弦黑洞区域都是定义明确且有界的：r_{最小值} leq r_+ \leq r_S, M_{最小值} \leq M_+ \leq M, T_H \leq T_+ \leq T_S. 该字符串“minimal”黑洞的寿命为 tau_{最小值} \simeq \frac{k_B c}{G \hbar} T^{-3}_S。 显示英文摘要

摘要： The quantum string emission by Black Holes is computed in the framework of the `string analogue model' (or thermodynamical approach), which is well suited to combine QFT and string theory in curved backgrounds (particulary here, as black holes and strings posses intrinsic thermal features and temperatures). The QFT-Hawking temperature T_H is upper bounded by the string temperature T_S in the black hole background. The black hole emission spectrum is an incomplete gamma function of (T_H - T_S). For T_H << T_S, it yields the QFT-Hawking emission. For T_H \to T_S, it shows highly massive string states dominate the emission and undergo a typical string phase transition to a microscopic `minimal' black hole of mass M_{\min} or radius r_{\min} (inversely proportional to T_S) and string temperature T_S. The semiclassical QFT black hole (of mass M and temperature T_H) and the string black hole (of mass M_{min} and temperature T_S) are mapped one into another by a `Dual' transform which links classical/QFT and quantum string regimes. The string back reaction effect (selfconsistent black hole solution of the semiclassical Einstein equations with mass M_+ (radius r_+) and temperature T_+) is computed. Both, the QFT and string black hole regimes are well defined and bounded: r_{min} leq r_+ \leq r_S, M_{min} \leq M_+ \leq M, T_H \leq T_+ \leq T_S. The string `minimal' black hole has a life time tau_{min} \simeq \frac{k_B c}{G \hbar} T^{-3}_S.