Electromagnetic field and spatially hyperbolical spacetime models

In this paper, we study the hyperbolically symmetric spacetime in the presence of an electric field to explore static analytical solutions of anisotropic self-gravitating objects. We analyze the effects of charged geometry-matter coupling on the finding of [L. Herrera, A. Di Prisco and J. Ospino, Phys. Rev. D 103(2) (2021) 024037]. Two distinct structural scalars are reckoned after splitting orthogonally the Riemann curvature tensor in the present gravitational corrections. The energy density associated with spatially hyperbolic anisotropic geometry is seen to be unavoidably less than zero, thereby indicating its relevance in the modeling of exotic structures, possibly near wormholes. We observe the different behavior of matter content near the axis of symmetry, giving rise to the formation of a cavity. The possible mathematical expression involved in maintaining the anisotropic system to experience a less complex and simple environment is calculated accompanied by the Weyl scalar. The effects of the electromagnetic field are observed in the theoretical models of conformally flat and simple geometric ideal structures. Furthermore, a spatially hyperbolic charged metric model is obtained which is assumed to be mediated by a barotropic state equation.