Kruskal-Penrose Formalism for Lightlike Thin-Shell Wormholes

TL;DR

This paper develops a Kruskal-Penrose formalism for lightlike thin-shell wormholes, extending the analysis of Einstein-Rosen bridges and revealing properties akin to QCD charge confinement.

Contribution

It provides a detailed Kruskal-Penrose description of lightlike thin-shell wormholes and generalizes it to more complex cases with two throats and charge confinement.

Findings

Explicit Kruskal-Penrose description of lightlike thin-shell wormholes.

Generalization to wormholes with two throats and QCD-like charge confinement.

Enhanced understanding of the spacetime structure of lightlike wormholes.

Abstract

The original formulation of the "Einstein-Rosen bridge" in the classic paper of Einstein and Rosen (1935) is historically the first example of a static spherically-symmetric wormhole solution. It is not equivalent to the concept of the dynamical and non-traversable Schwarzschild wormhole, also called "Einstein-Rosen bridge" in modern textbooks on general relativity. In previous papers of ours we have provided a mathematically correct treatment of the original "Einstein-Rosen bridge" as a traversable wormhole by showing that it requires the presence of a special kind of "exotic matter" located on the wormhole throat - a lightlike brane (the latter was overlooked in the original 1935 paper). In the present note we continue our thorough study of the original "Einstein-Rosen bridge" as a simplest example of a lightlike thin-shell wormhole by explicitly deriving its description in terms of the Kruskal-Penrose formalism for maximal analytic extension of the underlying wormhole spacetime manifold. Further, we generalize the Kruskal-Penrose description to the case of more complicated lightlike thin-shell wormholes with two throats exhibiting a remarkable property of QCD-like charge confinement.