Violation of Weak Cosmic Censorship in Einstein-Maxwell-dilaton theory: singularities connected by traversable wormholes

Abstract: We give two new analytical solutions to the low-energy string theory action that violate the weak cosmic censorship conjecture. They are classical charged solutions to the Einstein-Maxwell-dilaton theory in four dimensions that come in two types. The first represents one single naked singularity whose asymptotic region is flat. Its mass respects the positive mass theorem. The absence of horizons allows us to probe quantum aspects of gravity by direct observation of these singularities. The second represents singularities that come in pairs that "seem to create their own spacetime", and the region connecting them has the geometry of a traversable wormhole. In other words, they represent a pair of singularities connected by a traversable wormhole. The dyonic solution has a limit free of singularities, which we call "extremal limit" in analogy with black holes. This has a geometry given by the AdS$_{2}\times$S$^{2}$ spacetime in global coordinates. We compute the physical charges for the naked singularities and show that the weak gravity conjecture can be respected or violated, depending on the parameters of the solutions. We also compute the light deflection angle.