Quantum Fields, Geometric Fluctuations, and the Structure of Spacetime

TL;DR

This paper investigates how quantum vacuum fluctuations in a 2D dilaton gravity model cause spacetime geometry to fluctuate, leading to geodesic convergence and collapse, revealing the impact of quantum effects on spacetime structure.

Contribution

It demonstrates the influence of quantum vacuum fluctuations on spacetime geometry using a well-understood 2D model, linking quantum effects to geodesic behavior.

Findings

Quantum fluctuations cause spacetime to become 'fuzzy' and unstable.

Geodesic deviation analysis shows matter trajectories eventually collapse.

Results support earlier findings on null geodesic behavior in similar models.

Abstract

Quantum fluctuations of the vacuum stress-energy tensor are highly non-Gaussian, and can have unexpectedly large effects on spacetime geometry. In this paper, we study a two-dimensional dilaton gravity model coupled to a conformal field, in which the distribution of vacuum fluctuations is well understood. In this model, the fluctuations of the matter field are responsible for the fluctuations of the geometry itself. By analyzing the geodesic deviation in this model, we show that a pencil of massive particles propagating on this fuzzy spacetime eventually converges and collapses. This is consistent with our earlier analysis of null geodesics in [Phys. Rev. Lett.\ 107, 021303 (2011)].