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Simple method to generate magnetically charged ultra-static traversable wormholes without exotic matter in Einstein-scalar-Gauss-Bonnet gravity

All the magnetically charged ultrastatic and spherically symmetric spacetime solutions in the framework of linear/nonlinear electrodynamics, with an arbitrary electromagnetic Lagrangian density $\mathcal{L}(\mathcal{F})$ depending only of the electromagnetic invariant $\mathcal{F}\!=\!F_{αβ}F^{αβ}\!/4$, minimally coupled to Einstein-scalar-Gauss-Bonnet gravity [EsGB-$\mathcal{L}(\mathcal{F})$], are found. We also show that a magnetically charged ultrastatic and spherically symmetric EsGB-$\mathcal{L}(\mathcal{F})$ solution with invariant $\mathcal{F}$ having a strict global maximum value $\mathcal{F}_{_{0}}$ in the entire domain of the solution, and such that $\mathcal{L}_{_{0}}=\mathcal{L}(\mathcal{F}_{_{0}})>0$, can be interpreted as an ultrastatic wormhole spacetime geometry with throat radius determined by the scalar charge and the quantity $\mathcal{L}_{_{0}}$. We provide some examples, including Maxwell's theory of electrodynamics (linear electrodynamics) $\mathcal{L}_{_{_{\mathrm{LED}}}} \!=\! \mathcal{F}$, producing the magnetic dual of the purely electric Ellis-Bronnikov EsGB Maxwell wormhole derived in [P. Cañate, J. Sultana, D. Kazanas, Phys. Rev. D {\bf100}, 064007 (2019)]; and the nonlinear electrodynamics (NLED) models given by Born-Infeld $\mathcal{L}_{_{_{\mathrm{BI}}}} \!=\! -4β^{2} + 4β^{2} \sqrt{ 1 + \mathcal{F}\!/\!(2β^{2})~}$, and Euler-Heisenberg in the approximation of the weak-field limit $\mathcal{L}_{_{_{\mathrm{EH}}}} \!=\! \mathcal{L}_{_{_{\mathrm{LED}}}} + γ\mathcal{F}^{2}\!/2$. With those NLED models, two novel magnetically charged ultrastatic traversable wormholes (EsGB Born-Infeld and EsGB Euler-Heisenberg wormholes) are presented as exact solutions without exotic matter in EsGB-$\mathcal{L}(\mathcal{F})$ gravity.