Quantum Fluctuations and Curvature Singularities in Jackiw-Teitelboim Gravity

TL;DR

This paper explores how quantum effects in Jackiw-Teitelboim gravity lead to the formation of curvature singularities, which are absent classically, and analyzes their implications for gravitational scattering and spacetime structure.

Contribution

It provides an exact solution for the quantum-corrected model, demonstrating the emergence of curvature singularities due to quantum effects in a solvable 2D gravity framework.

Findings

Quantum corrections induce curvature singularities in solutions.

Classical solutions are free of singularities for most cases.

Exact effective action obtained for N=24 matter fields.

Abstract

The Jackiw-Teitelboim gravity with the matter degrees of freedom is considered. The classical model is exactly solvable and its solutions describe non-trivial gravitational scattering of matter wave-packets. For huge amount of the solutions the scattering space-times are free of curvature singularities. However, the quantum corrections to the field equations inevitably cause the formation of (thunderbolt) curvature singularities, vanishing only in the limit $\hbar\to 0$. The singularities cut the space-time and disallow propagation to the future.The model is inspired by the dimensional reduction of 4-d pure Einstein gravity, restricted to the space-times with two commuting space-like Killing vectors. The matter degrees of freedom also stem from the 4-d ansatz. The measures for the continual integrations are judiciously chosen and one loop contributions (including the graviton and the dilaton ones) are evaluated. For the number of the matter fields $N=24$ we obtain even the exact effective action, applying the DDK-procedure. The effective action is nonlocal, but the semiclassical equations can be solved by using some theory of the Hankel transformations.