Orthogonal splitting of the Riemann curvature tensor and implications of resulting scalar(s) on compact stellar evolution

Abstract In this work, a charged fluid system is studied by employing the complexity factor formalism for a static spherical spacetime. We proceed by calculating two distinct mass functions and obtaining the Einstein field equations for the anisotropic fluid. Following Herrera’s methodology, we designate $${Y}_{TF}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Y</mml:mi> <mml:mrow> <mml:mi>TF</mml:mi> </mml:mrow> </mml:msub> </mml:math> as the complexity factor as it integrates the two fundamental dynamic components like the density inhomogeneity and pressure anisotropy. Additionally, the field equations are addressed by applying a few constraints, with the first being the condition of zero complexity. By implementing two distinct forms for the radial metric potential, we derive two independent solutions. The unknowns involved in these models are then found using the junction conditions by taking into account the Reissner–Nordström exterior metric. Subsequently, observed data from multiple stars is used to generate a visual depiction of the obtained solutions. Our analysis demonstrates that both proposed models maintain physically stable and viable profiles, highlighting the critical role of the vanishing complexity condition in constructing anisotropic fluid solutions under the presence of an electric charge.