Charged Ellis Wormhole and Black Bounce

Abstract

By replacing the scalar $\phi$ with $i\phi$ in the solution constructed in Ref\cite{Huang:2019lsl}, we obtain electrically-charged wormhole and black hole solutions in the Einstein-Maxwell-scalar theory, in which the scalar is a phantom field coupled to the Maxwell field non-minimally. Our solutions are simpler than the previously-known charged wormholes in the Einstein-Maxwell-dilaton theory in that both the scalar and the radius of the foliating sphere of our solutions are independent of electric charge. The wormhole solution has two asymptotically flat regions and reduces to Ellis wormhole when the charge is zero. We draw the embedding diagrams for the wormholes and demonstrate that the two sides are asymmetric. As the charge increases, horizons will appear, and the wormhole becomes a black hole, with no curvature singularity but a wormhole throat or a bounce. We analyze black hole thermodynamics and the causal structure. We also determine the photon spheres of both the wormhole and the black hole and discuss their observable characteristics.