Einstein–Rosen “bridge” needs lightlike brane source

Abstract

The Einstein–Rosen “bridge” wormhole solution proposed in the classic paper (Einstein and Rosen (1935) [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.