This study explores the behavior of an anisotropic fluid in a spherically symmetric spacetime by examining expanding and collapsing solutions to the Einstein Field Equations (EFEs) within the framework of if(R,T)/i gravity. This modified theory of gravity extends General Relativity by allowing the gravitational action to depend on both the Ricci scalar iR/i and the trace iT/i of the energy-momentum tensor. The work incorporates a cosmological constant to assess its influence on the evolution of the fluid. A central aim of the study is to understand how the interaction between the Ricci scalar, the expansion scalar, and the trace of the energy-momentum tensor affects the dynamics of the system. Special attention is given to the anisotropic nature of the fluid, where radial and tangential pressures differ adding complexity to both expansion and collapse processes. The presence of a cosmological constant further modifies the pressure and density profiles, revealing how dark energy-like effects can shape the evolution of matter under gravity. The research identifies the existence of a single horizon in the system and uses a mass function to analyze the formation of trapped surfaces regions where outgoing light rays begin to converge, indicating gravitational collapse. Additionally, the relationship between the coupling constants Λ (cosmological constant) and iλ/i (associated with the if(R,T)/i theory) is explored for both collapsing and expanding scenarios. Graphical results highlight the influence of these parameters on pressure, mass, anisotropy, and energy density, offering valuable insights into modified gravity’s role in astrophysical phenomena.
Khan et al. (Wed,) studied this question.