Kruskal–Penrose Formalism for Lightlike Thin-Shell Wormholes

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.