Anisotropic fluid dynamics with vanishing complexity and expansion-free constraints: Exploring analytical solutions in charged modified gravity

Abstract

In this paper, we study non-static spherically symmetric shear-free anisotropic dissipative fluid distribution coupled with Maxwell field equations to find the solutions for dynamical equations Herrera et al. (2023) in $f\left(R\right)$ gravity and use a physically realistic model, i.e., $f\left(R\right)=R+\delta R^2$, where $R$ represents the Ricci scalar. We compute gravitational mass (Misner–Sharp) to explore matching conditions. We also construct conservation equations for ordinary, effective dark source terms and electromagnetic stress–energy tensors using Bianchi identities in $f\left(R\right)$ gravity. Further, we utilize constraints like vanishing expansion scalar and complexity factor to derive exact analytical solutions for gravitational equations in $f\left(R\right)$ gravity.