Topological dressing method for the Einstein–Maxwell equations

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 a thin-shell wormhole, but unlike it, it is exact and therefore does not require the presence of any other field sources. It is shown that the wormhole itself creates both gravitational and electromagnetic fields. The corresponding effective mass and effective charge are distributed over the surface of its throat and around it. Topological dressing of the Reissner–Nordström solution with zero effective mass and non-zero effective charge gives a new solution describing a traversable wormhole. It is shown that this solution is stable in the presence of external pressure.