The Non-Perturbative Hilbert Space of JT Gravity

We propose a non-perturbative construction of the bulk Hilbert space of JT gravity. Within this Hilbert space, we can non-perturbatively define and study observables that probe the black hole interior. To exemplify the power of this construction, we discuss two related observables for two-sided black holes: one probes the length of the black hole interior, and the other probes the center of mass collision energy between an observer infalling from one side and a shockwave coming from the opposite side. As we shall discuss, both observables are strongly affected by non-perturbative corrections at very late times, serving as useful probes for the presence of firewalls in very old black holes.