Implications of vanishing complexity condition in $$f({\textbf{R}})$$ f ( R ) theory

Abstract

Abstract This paper introduces the concept of complexity for a static spherical spacetime and extends it to the modified $$f({\textbf{R}})$$ f ( R ) framework. The formulation of the corresponding field equations is then carried out to describe the anisotropic interior. The spherical mass function is defined in both geometric as well as matter terms. Utilizing the orthogonal splitting of the curvature tensor, specific scalars are developed, with one of them denoted as $${\mathcal {Y}}_{TF},$$ Y TF , identified as the complexity factor for the considered fluid setup. In addressing the system of field equations admitting some extra degrees of freedom, the complexity-free condition is introduced. In conjunction with this condition, three other constraints are applied, leading to the development of different models. We also provide a graphical representation of the resulting solutions, using specific parametric values. From this analysis, we conclude that our all three models exhibit the properties required for the existence of physically viable and stable structures for certain values of the model parameter.