New exact traversable wormhole solution to the Einstein-scalar-Gauss-Bonnet Equations coupled to a power-Maxwell electrodynamics

Abstract

We present a novel, exact, traversable wormhole (T-WH) solution for $(3+1)$-dimensional Einstein-scalar-Gauss-Bonnet theory (EsGB) coupled to a power-Maxwell nonlinear electrodynamics (NLED). The solution is characterized by two parameters, $\mathcal{Q}{}_{\mathrm{e}}$ and $\mathcal{Q}{}_{{}_{\mathcal{S}}}$, associated respectively with the electromagnetic field and the scalar field. We show that for ${\mathcal{Q}}_{\mathrm{e}}^2-\mathcal{Q}{}_{{}_{\mathcal{S}}}>0$ the solution can be interpreted as a traversable wormhole. In the general case, with non-vanishing electromagnetic field, the scalar-Gauss-Bonnet term (sGB) is the only responsible for the negative energy density necessary for the traversability. In the limiting case of vanishing electromagnetic field, the scalar field becomes a phantom one keeping the WH throat open and in this case the Ellis WH solution \cite{Ellis} is recovered.

8 pages, 2 figures