标题： 温度和量子黑洞的熵以及共形异常 显示英文标题

标题： Temperature and Entropy of a Quantum Black Hole and Conformal Anomaly

摘要： 注意经典黑洞的温度可以从其自由能相对于黑洞质量变化的极端条件中推导出来。 对于蒸发无质量粒子的量子施瓦茨希尔德黑洞，同样的条件被证明会导致以下一环温度$T=(8\pi M)^{-1} (1+\sigma (8\pi M^2)^{-1})$和熵$S = 4\pi M^2 - \sigma\log M$，这些量用黑洞的有效质量$M$以及其辐射和与场种类有关的共形异常积分$\sigma$表示。 因此，在这种情况下，$T$和$S$的量子修正完全由异常提供。 当不存在（$\sigma=0$）时，这在许多超对称模型中会发生，一环情况下$T$和$S$的表达式保持经典形式。 另一方面，如果反常为负（$\sigma<0$），当黑洞质量达到普朗克尺度时，蒸发的量子洞似乎不再继续升温。 显示英文摘要

摘要： Attention is paid to the fact that temperature of a classical black hole can be derived from the extremality condition of its free energy with respect to variation of the mass of a hole. For a quantum Schwarzschild black hole evaporating massless particles the same condition is shown to result in the following one-loop temperature $T=(8\pi M)^{-1} (1+\sigma (8\pi M^2)^{-1})$ and entropy $S = 4\pi M^2 - \sigma\log M$ expressed in terms of the effective mass $M$ of a hole together with its radiation and the integral of the conformal anomaly $\sigma$ that depends on the field species. Thus, in the given case quantum corrections to $T$ and $S$ turn out to be completely provided by the anomaly. When it is absent ($\sigma=0$), which happens in a number of supersymmetric models, the one-loop expressions of $T$ and $S$ preserve the classical form. On the other hand, if the anomaly is negative ($\sigma<0$) an evaporating quantum hole seems to cease to heat up when its mass reaches the Planck scales.