Interpretation of complexity for spherically symmetric fluid composition within the context of modified gravity theory

TL;DR

This paper explores the concept of complexity in spherically symmetric fluid distributions within a modified gravity framework, deriving new equations and analyzing how anisotropy and inhomogeneity influence complexity.

Contribution

It extends the interpretation of complexity to $f(R, abla_m, abla_T)$ gravity, deriving modified field equations and analyzing the complexity factor in this context.

Findings

Complexity is linked to anisotropy and inhomogeneity in matter distribution.

Certain solutions show diminishing complexity with specific scalar conditions.

Dark source terms can reduce the perceived complexity in the model.

Abstract

Regardless of the adequate descriptions of complexity in distinct alternative gravity theories, its elaboration in the framework of $f(R,\mathcal{L}_{m},\mathcal{T})$ theory remains uncertain. The orthogonal splitting of the curvature tensor yields the complexity factor as suggested by Herrera \cite {herrera2018new}. To commence our study, the inner spacetime is assumed to be spherically symmetric static composition comprised of the anisotropic fluid. In this context, we derive the modified field equations for the considered theory and take into account the established relationship between the conformal and curvature tensors to interpret the complexity. Furthermore, we determine the correspondence of the mass functions with the complexity factor, represented by a specific scalar $Y_{TF}$. Certain solutions complying with the precedent of diminishing $Y_{TF}$ are also evaluated. It is noted that celestial formations having anisotropic and non-uniform compositions of matter assert the utmost complexity. Nevertheless, the spherically symmetric matter distribution may not exhibit complexity in the scenario of vanishing impacts of non-homogenous energy density and anisotropic pressure due to the presence of dark source terms associated with this extended gravity theory.