On the non-perturbative bulk Hilbert space of JT gravity

TL;DR

This paper defines a non-perturbative bulk Hilbert space for 2D JT gravity, including matter, and studies the behavior of certain operators related to black hole interiors, revealing insights into late-time black hole physics.

Contribution

It provides an explicit non-perturbative Hilbert space construction for JT gravity with matter, identifying null states and analyzing non-perturbative effects on black hole interior proxies.

Findings

Null states are explicitly identified and their importance discussed.

Operators related to black hole interiors show spreading at late times.

There is an O(1) probability of detecting a firewall at late times.

Abstract

What is the bulk Hilbert space of quantum gravity? In this paper, we resolve this problem in 2d JT gravity, both with and without matter, providing an explicit definition of a non-perturbative Hilbert space specified in terms of metric variables. The states are wavefunctions of the length and matter state, but with a non-trivial and highly degenerate inner product. We explicitly identify the null states, and discuss their importance for defining operators non-perturbatively. To highlight the power of the formalism we developed, we study the non-perturbative effects for two bulk linear operators that may serve as proxies for the experience of an observer falling into a two-sided black hole: one captures the length of an Einstein-Rosen bridge and the other captures the center-of-mass collision energy between two particles falling from opposite sides. We track the behavior of these operators up to times of order $e^{S_\text{BH}}$, at which point the wavefunction spreads to the complete set of eigenstates of these operators. If these observables are indeed good proxies for the experience of an infalling observer, our results indicate an O(1) probability of detecting a firewall at late times that is self-averaging and universal.