Field sources for Simpson-Visser space-times

Abstract

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 $V(\varphi )$ and a magnetic field in the framework of nonlinear electrodynamics with the Lagrangian $\mathcal{L}(\mathcal{F})$, $\mathcal{F}=F_{\mu \nu }{F}^{\mu \nu }$ (in standard notations). Explicit forms of $V(\varphi )$ and $\mathcal{L}(\mathcal{F})$ are presented for the cases of Schwarzschild-like and Reissner-Nordstrom-like SV metrics.

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