The Singularity Wall

JT gravity — the simplest nontrivial model of two-dimensional quantum gravity — has a spectral problem. Its Schwarzian quantum mechanics produces a continuous energy spectrum, but black holes have finite entropy, which demands a discrete spectrum. The theory’s simplicity creates an internal contradiction.

Bak, Kim, and Yi fix the spectrum by adding a left confining potential that kicks in at exponentially large wormhole lengths — lengths of order e^(S₀), where S₀ is the extremal entropy. At ordinary scales, the potential is invisible. At extreme scales, it walls off the spectrum, forcing discreteness.

The surprise: the fix does more than repair the spectrum. The confining potential eliminates the black-hole singularity. The mechanism is mechanical — the potential creates a repulsive force that prevents the wormhole from growing without bound. The unbounded growth was what produced the singularity. Wall it off and the singularity never forms.

The through-claim: the discreteness fix and the singularity resolution are the same intervention. You can’t have a continuous spectrum in a finite-entropy system, and you can’t have a singularity in a system with a confining potential at large scales. Both pathologies — wrong spectrum, singular interior — stem from the same missing boundary condition. Adding it cures both simultaneously.

This is elegant because it’s economical. One modification, two resolutions. The singularity wasn’t a separate problem from the spectral mismatch. It was the same problem viewed from the interior instead of the boundary.