Simple method to generate magnetically charged ultra-static traversable wormholes without exotic matter in Einstein-scalar-Gauss-Bonnet gravity (2310.08758v2)

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. Ca~nate, 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.