Einstein-Rosen "Bridge" Needs Lightlike Brane Source

TL;DR

This paper demonstrates that the Einstein-Rosen wormhole solution requires a lightlike brane source at the throat to satisfy Einstein's equations, resolving inconsistencies in the original vacuum solution.

Contribution

It introduces a consistent formulation of the Einstein-Rosen bridge involving a lightlike brane, clarifying the source of the wormhole at the throat.

Findings

The Einstein-Rosen bridge needs a lightlike brane source at the throat.

The brane's stress-energy tensor matches the Einstein equations at the throat.

The approach resolves the vacuum inconsistency of the original wormhole solution.

Abstract

The Einstein-Rosen "bridge" wormhole solution proposed in the classic paper [1] does not satisfy the vacuum Einstein equations at the wormhole throat. We show that the fully consistent formulation of the original Einstein-Rosen "bridge" requires solving Einstein equations of bulk D=4 gravity coupled to a lightlike brane with a well-defined world-volume action. The non-vanishing contribution of Einstein-Rosen "bridge" solution to the right hand side of Einstein equations at the throat matches precisely the surface stress-energy tensor of the lightlike brane which automatically occupies the throat ("horizon straddling") - a feature triggered by the world-volume lightlike brane dynamics.