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 L(F) depending only of the electromagnetic invariant F\!=\!FαβFαβ\!/4, minimally coupled to Einstein-scalar-Gauss-Bonnet gravity [EsGB-L(F)], are found. We also show that a magnetically charged ultrastatic and spherically symmetric EsGB-L(F) solution with invariant F having a strict global maximum value F_0 in the entire domain of the solution, and such that L_0=L(F_0)>0, can be interpreted as an ultrastatic wormhole spacetime geometry with throat radius determined by the scalar charge and the quantity L_0. We provide some examples, including Maxwell's theory of electrodynamics (linear electrodynamics) L_LED \!=\! 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 100, 064007 (2019)]; and the nonlinear electrodynamics (NLED) models given by Born-Infeld L_BI \!=\! -4β2 + 4β2 1 + F\!/\!(2β2)~, and Euler-Heisenberg in the approximation of the weak-field limit L_EH \!=\! L_LED + γ F2\!/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-L(F) gravity.
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