Field sources for Simpson-Visser space-times

Simpson-Visser (SV) space-times are the simplest globally regular modifications of the Schwarzschild, Reissner-Nordstrom and other blak-hole solutions of general relativity. They smoothly interpolate between these black holes and traversable wormholes. After a brief presentation of the Schwarzschild-like and Reissner-Nordstrom-like SV geometries, including their Carter-Penrose diagrams, we show that any static, spherically symmetric SV metric can be obtained as an exact solution to the Einstein field equations sourced by a combination of a minimally coupled phantom scalar field with a nonzero potential $V(ϕ)$ and a magnetic field in the framework of nonlinear electrodynamics with the Lagrangian $\mathcal {L(F)}$, $\mathcal{F} = F_{μν} F^{μν}$ (in standard notations). Explicit forms of $V(ϕ)$ and $\mathcal {L(F)}$ are presented for the cases of Schwarzschild-like and Reissner-Nordstrom-like SV metrics.

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