Wormholes in the non-minimally coupled gravity with electromagnetism

Since the general relativistic approach requires exotic matter with negative energy density, constructing wormholes containing realistic matter is a crucial challenge. Therefore, extending General Relativity to non-minimal cases may be an alternative option. In this paper, we investigate wormholes which are supported by the non-minimally coupled electromagnetic fields to gravity in $Y\left(R\right)F^2$ form where $F^2$ is the Maxwell invariant and $Y\left(R\right)$ is a function of the Ricci scalar R. We consider both electrically and magnetically charged cases. Then we give some exact asymptotically AdS/dS and flat solutions for traversable wormhole geometries. By discussing whether these obtained geometries satisfy the energy conditions and vanishing sound speed condition, we determine stable solutions containing realistic matter for some parameter values.