Black holes that have nearly 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. In this article, we expand on previous results and show that finding the maximal surfaces in an arbitrary spherically symmetric spacetime is equivalent to a 1+1 geodesic problem. We then study the effect of Hawking radiation on the volume by computing the volume of maximal surfaces inside the apparent horizon of an evaporating black hole as a function of time at infinity: while the area is shrinking, the volume of these surfaces grows monotonically with advanced time, up to when the horizon has reached Planckian dimensions. The physical relevance of these results for the information paradox and the remnant scenarios are discussed.And then, from within the paper itself:
A few numbersImpressive, to put it mildly.
Before closing this section, let us put the above in perspective: when a solar mass (1030 kg) black hole becomes Planckian (it needs 1055 times the actual age of the universe), it will contain volumes equivalent to 105 times our observable universe, hidden behind a Planckian area (10−70 m2).
Perhaps more pertinent is to consider small primordial black holes with mass less than 1012 kg. Their initial horizon radius and volume are of the order of the proton charge radius (10−15m) and volume (10−45m3) respectively. They would be in the final stages of evaporation now, hiding volumes of about one litre (10−9m3).