标题： 黑洞背景中量子场的熵 显示英文标题

标题： On the Entropy of Quantum Fields in Black Hole Backgrounds

摘要： 我们证明了标量场在静态时空背景下的配分函数可以表示为相应光学空间中的泛函积分，并指出这与原始度规下的泛函积分之差是一个Liouville型作用量。 在高温近似下推导出自由能的一般公式，并将其应用于各种情况。 特别是，我们发现极端Reissner-Nordström空间中的热力学存在额外的奇异性，使其定义不良。 显示英文摘要

摘要： We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral in the original metric is a Liouville type action. A general formula for the free energy is derived in the high temperature approximation and applied to various cases. In particular we find that thermodynamics in the extremal Reissner-Nordstr\"om space has extra singularities that make it ill-defined.