Black holes and revelations: their large interiors

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The 3d volume inside a spherical black hole can be defined by extending an intrinsic flat-spacetime characterization of the volume inside a 2-sphere. For a collapsed object, the volume grows with time since the collapse, reaching a simple asymptotic form, which has a compelling geometrical interpretation. Perhaps surprising, it is large. The result may have relevance for the discussion on the information paradox.
Marios Christodoulou & Carlo Rovelli (2014). How big is a black hole?, arXiv:
A sphere $S$ on the event horizon bounds a spacelike hypersurface, a large portion of which coincides with an $r$ = constant hypersurface. We show this hypersurface with one dimension suppressed, and cut in the middle, omitting the long cylindrical part which gives the main contribution to its volume. We also illustrate the argument showing that most of the volume is contained in a region out of causal contact with matter that has advanced far into the black hole.
Ingemar Bengtsson & Emma Jakobsson (2015). Black holes: Their large interiors, arXiv:

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