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Understanding the fate of semi-classical black hole solutions at very latetimes is one of the most important open questions in quantum gravity. In thispaper, we provide a path integral definition of the volume of the black holeinterior and study it at arbitrarily late times for black holes in variousmodels of two-dimensional gravity. Because of a novel universal cancellationbetween the contributions of the semi-classical black hole spectrum and some ofits non-perturbative corrections, we find that, after a linear growth at earlytimes, the length of the interior saturates at a time, and towards a value,that is exponentially large in the entropy of the black hole. This provides anon-perturbative confirmation of the complexity equals volume proposal sincecomplexity is also expected to plateau at the same value and at the same time.

The volume of the black hole interior at late times