Consequences of electric charge on anisotropic hyperbolically symmetric static spacetime

The investigation of hyperbolically symmetric sources under the impact of electromagnetic field is conducted in this paper, with a focus on the fluid distributed in static spacetime. To do this, we choose the metric f(R) gravity. It is observed that the fluid does not have the capacity to occupy the space surrounding the center, meaning that it exhibits cavity around the core. Furthermore, calculating the energy density indicates that it is invariably negative in the presence of correction terms, which might be crucial in comprehending certain quantum field occurrences, due to the fact that negative energies are directly tied with the quantum field theory. In this modified gravity, we implement the orthogonal splitting of the curvature tensor and derive the structure scalars. Following that, some cosmological models exhibiting the hyperbolical symmetry as well as their substantial determinants are investigated using two generating functions. The model of less-complex relativistic system of Einstein gravity is offered to explore precisely the role of f(R) terms under the influence of electromagnetic field.