Topological dressing method for the Einstein-Maxwell equations

Abstract: A regular method is proposed that makes it possible to obtain a new exact solution with a wormhole from any topologically trivial exact solution of the Einstein-Maxwell equations in an electrovacuum (topological dressing method). This solution has a structure similar to that of a thin-shell wormhole, but unlike it, it is exact and, therefore, does not require the presence of any other field sources. The wormhole itself is shown to create both gravitational and electromagnetic fields. The corresponding effective mass and effective charge are distributed over the surface of its throat and around it. The topological dressing of the Reissner-Nordstr\"om solution with zero effective mass and non-zero effective charge gives a new solution describing a traversable wormhole. This solution is shown to be stable in the presence of external pressure.