The volume of quasi-static spherically symmetric charged black hole

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.