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

Author:

Pedro Cañate

Keyword:

General Relativity and Quantum Cosmology, General Relativity and Quantum Cosmology (gr-qc)

journal:

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date:

2023-10-11 16:00:00

Abstract

All the magnetically charged ultra-static 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 ultra-static and spherically symmetric EsGB-$\mathcal{L}(\mathcal{F})$ solution with invariant $\mathcal{F}$ having a strict global maximum value $\mathcal{F}_{_{0}}$ in entire domain of the solution, and such that $\mathcal{L}_{_{0}}=\mathcal{L}(\mathcal{F}_{_{0}})>0$, can be interpreted as an ultra-static wormhole spacetime geometry with throat radius determines in function of 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 100, 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 ultra-static 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.