标题： 锥形奇点与黑洞熵的量子修正 显示英文标题

标题： The Conical Singularity And Quantum Corrections To Entropy Of Black Hole

摘要： 对于不同于霍金温度的一般有限温度，引力方程的欧几里得经典解中会出现一个众所周知的锥形奇点。通过正则曲面来正则化锥形的方法被用来确定此类度规的曲率张量。这使得我们能够在吉布斯和霍金的路径积分方法框架内计算物质的有效作用量的一圈修正以及相应的熵的一圈量子修正。考虑了二维和四维的情况。结果显示，二维Rindler空间的熵对数发散，而四维情况下则是二次发散，这与之前得到的结果一致。对于永恒的二维黑洞，我们观察到熵存在依赖于质量的有限修正。四维Schwarzschild黑洞的熵显示出一个额外的（与四维Rindler空间相比）对数发散修正，即使在黑洞质量趋于无穷大的极限下也不会消失。我们认为，四维情况下熵的发散可以通过重正化引力耦合来消除。 显示英文摘要

摘要： For general finite temperature different from the Hawking one there appears a well known conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such a metrics. This allows one to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions that coincides with results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison with the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized by the renormalization of the gravitational coupling.