标题： 黑洞的体积 显示英文标题

标题： The Volume of Black Holes

摘要： 我们提出了一种静态时空体积的定义。所提出的体积与静止时间切片的选择无关，即使 Killing 向量可能并非全局时向也适用。此外，它在时间上是恒定的，并且非常简单：四维球对称黑洞的体积恰好为${4 \over 3} \pi r_+^3$。然后我们考虑是否可以通过将半径发送到无穷大同时进行离散识别以保持视界面积来构造具有有限视界面积但无限体积的时空。我们证明，在三维或四维情况下，不存在不以某种方式不一致的此类解。我们讨论了这对贝肯斯坦-霍金熵的解释的影响。 显示英文摘要

摘要： We propose a definition of volume for stationary spacetimes. The proposed volume is independent of the choice of stationary time-slicing, and applies even though the Killing vector may not be globally timelike. Moreover, it is constant in time, as well as simple: the volume of a spherical black hole in four dimensions turns out to be just ${4 \over 3} \pi r_+^3$. We then consider whether it is possible to construct spacetimes that have finite horizon area but infinite volume, by sending the radius to infinity while making discrete identifications to preserve the horizon area. We show that, in three or four dimensions, no such solutions exist that are not inconsistent in some way. We discuss the implications for the interpretation of the Bekenstein-Hawking entropy.