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

Abstract

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 $\mathcal{F}=F_{\alpha \beta }{F}^{\alpha \beta }/4$, 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 ${\mathcal{L}}_{{}_{{}_{\mathrm{BI}}}}=-4{\beta }^2+4{\beta }^2\sqrt{1+\mathcal{F}/(2{\beta }^2)}$, and Euler-Heisenberg in the approximation of the weak-field limit ${\mathcal{L}}_{{}_{{}_{\mathrm{EH}}}}={\mathcal{L}}_{{}_{{}_{\mathrm{LED}}}}+\gamma {\mathcal{F}}^2/2$. 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.

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