Abstract Black holes that have evaporated are often thought of as small objects due to their tiny exterior area. However, the horizon bounds large spacelike hypersurfaces. A compelling geometric perspective on the evolution of the interior geometry was recently shown to be provided by a generally covariant definition of the volume inside a black hole using maximal surfaces. The case of an evaporating black hole has been illustrated. In this article, we expand on previous results in a different way and give a general method for solving the volume of a quasi-static spherically symmetric black hole. Our results are the same as before, while the area is shrinking, the volume of these surfaces grows monotonically with advanced time. However, the volume tends to be constant over time rather than proportional to time. The physical relevance of these results for the information paradox and the remnant scenarios is discussed.

中文翻译：

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准静态球对称带电黑洞的体积

摘要 蒸发的黑洞由于其外部面积很小，因此通常被认为是小物体。然而，地平线限制了大的类空间超曲面。最近证明了一个关于内部几何演化的引人注目的几何视角是由使用最大表面的黑洞内部体积的一般协变定义提供的。已经说明了蒸发黑洞的情况。在本文中，我们以不同的方式扩展了先前的结果，并给出了求解准静态球对称黑洞体积的一般方法。我们的结果和以前一样，虽然面积在缩小，但这些表面的体积随着时间的推移单调增长。然而，体积随着时间的推移趋于恒定而不是与时间成正比。