Field sources for Simpson-Visser spacetimes
К. А. Бронников, Rahul Kumar
Abstract
Simpson-Visser (SV) spacetimes are the simplest globally regular modifications of the Schwarzschild, Reissner-Nordsr\"om and other black 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-Nordsr\"om-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 $V(\ensuremath{\phi})$ and a magnetic field in the framework of nonlinear electrodynamics with the Lagrangian $\mathcal{L}(F)$, $\mathcal{F}={F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$ (in standard notations). Explicit forms of $V(\ensuremath{\phi})$ and $\mathcal{L}(F)$ are presented for the cases of Schwarzschild-like and Reissner-Nordsr\"om-like SV metrics.