An Effective Model of the Spacetime Foam

Abstract

The notion of a spacetime foam was introduced by Wheeler [1,2] for the description of the possible complex structure of the spacetime on the Planck scale (L _pl ≈ 10-³³cm). This hypothesized spacetime foam is a set of quantum wormholes (WH) (handles) appearing in the spacetime on the Planck scale level (see Fig.l). For the macroscopic observer these quantum fluctuations are smoothed and we have an ordinary smooth manifold with the metric submitting to Einstein equations. The exact mathematical description of this phenomenon is very difficult and even though there is a doubt: does the Feynman path integral in the gravity contain a topology change of the spacetime? This question spring up because (according to the Morse theory) the singular points must arise by the topology change. In such points the time arrow is undefined that leads in difficulties at definition of the Lorentzian metric, curvature tensor and so on. The main goal of this paper is to submit an effective model ofthe spacetime foam.