Würzburg Seminar on Quantum Field Theory and Gravity

Understanding the fate of semi-classical black hole solutions at very late times is one of the most important open questions in quantum gravity. In this paper, we provide a path integral definition of the volume of the black hole interior and study it at arbitrarily late times for black holes in various models of two-dimensional gravity. Because of a novel universal cancellation between the contributions of the semi-classical black hole spectrum and some of its non-perturbative corrections, we find that, after a linear growth at early times, the length of the interior saturates at a time, and towards a value, that is exponentially large in the entropy of the black hole.  I will additionally discuss why the volume is a self-averaging quantity and the consequences for gravitational theories in which the factorization puzzle is resolved. This provides non-perturbative evidence for the complexity equals volume proposal since complexity is also expected to plateau at the same value and at the same time.