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

## TL;DR

This paper introduces an exact traversable wormhole solution within Einstein-scalar-Gauss-Bonnet theory coupled to nonlinear electrodynamics, highlighting the role of scalar and electromagnetic fields in maintaining wormhole structure.

## Contribution

The work provides the first exact traversable wormhole solution in Einstein-scalar-Gauss-Bonnet theory coupled to power-Maxwell electrodynamics, detailing conditions for traversability and energy requirements.

## Key findings

- Solution characterized by electromagnetic and scalar field parameters.
- Scalar-Gauss-Bonnet term enables negative energy density for traversability.
- Special case recovers Ellis wormhole with phantom scalar field.

## 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, $\mathcal{Q}\!_{\rm e}$ and $\mathcal{Q}\!_{_{ \mathcal{S} }}$, associated respectively with the electromagnetic field and the scalar field. We show that for $\mathcal{Q}^2_{\rm e} - \mathcal{Q}\!_{_{ \mathcal{S} }}>0$ 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.