Resolution of Black Hole Singularities in Jackiw-Teitelboim Gravity

Abstract

In Jackiw-Teitelboim gravity, the naive Schwarzian quantum mechanics leads to a continuous bulk spectrum, in apparent contradiction with the finite entropy of the black hole, which requires a discrete spectrum with level spacing of order $e^{-S_0}$. It was recently shown that restoring spectral discreteness with random statistics requires the introduction of a left confining potential that becomes relevant when the renormalized wormhole length reaches order $e^{S_0}$. In this work, we show how the known perturbative results of JT gravity are recovered within this modified framework. More importantly, we demonstrate that this modification has a direct dynamical consequence: it resolves the black-hole singularity. The confining potential generates a repulsive force at exponentially large wormhole length, preventing the indefinite growth that would otherwise lead to a singularity. We explain in detail how this turnaround arises and explore its implications for late-time bulk gravitational dynamics, the disappearance of horizons, and possible observational consequences.

Figures (4)

• Figure 1: Penrose diagram of bulk AdS$_{2}$ spacetime with horizons and boundary cutoff trajectories.
• Figure 2: A schematic form of the potential $V(q)=e^q+W(q)$, where the left confining potential $W(q)$ becomes $O(1)$ only when $q$ becomes of $-O(e^{S_0})$. With the left confining potential, the spectrum becomes discrete.
• Figure 3: Schematic diagram for complexity vs time. The typical behavior of ramp, top, slope and plateau of the complexity or equivalently the geodesic length is depicted.
• Figure 4: The boundary cutoff trajectories, depicted by blue lines, do not touch the AdS boundaries depicted by black lines, and extend to the upper and lower sides forever. The dashed diagonal lines denote the would-be horizons and the dotted red lines do the would-be singularities.