Firewalls in the non-perturbative bulk Hilbert space of JT gravity

It has been shown that a very old black hole can tunnel into a white hole through the emission of a large baby universe. This process can be modeled by a genus-one geometry corresponding to a single baby universe emission, with a tunneling probability proportional to $t^{2} e^{-2S(E)}$, where $t$ denotes the black hole age and $S(E)$ its entropy at energy $E$. The growth of this probability at late times raises the question of its behavior near $t \sim e^{S}$. A natural possibility is that the full genus expansion, together with its non-perturbative completion, leads to saturation of the tunneling probability. Motivated by this idea, the present analysis employs a non-perturbative bulk inner product in place of the perturbative one and shows that, at late times, the probabilities of realizing firewall geometries and smooth geometries approach constant values.