Field sources for Simpson-Visser space-times

TL;DR

This paper demonstrates that Simpson-Visser space-times, which smoothly connect black holes and wormholes, can be exactly modeled as solutions to Einstein's equations with specific scalar and magnetic field sources.

Contribution

It provides explicit forms of the scalar potential and nonlinear electrodynamics Lagrangian for Simpson-Visser geometries, establishing their matter source models.

Findings

SV space-times are solutions with phantom scalar and magnetic fields.

Explicit potentials and Lagrangians are derived for Schwarzschild-like and Reissner-Nordstrom-like cases.

SV geometries can be realized as exact Einstein field solutions with specified matter sources.

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