Completely Deformed Complexity-free Anisotropic Fluid Sphere

TL;DR

This paper introduces a novel method combining zero-complexity and density constraints within gravitational decoupling to model anisotropic stellar structures, resulting in new solutions that are stable and physically viable.

Contribution

It presents a new synthesis of techniques for controlling anisotropy and complexity in stellar models, advancing the understanding of compact object internal structures.

Findings

Derived two new anisotropic solutions that satisfy stability and energy conditions

Demonstrated the unique role of the deformation parameter in energy transfer

Highlighted the influence of anisotropy on stellar stability

Abstract

In this work, we investigate the emergence of compact, anisotropic stellar structures through the gravitational decoupling scheme within the framework of complete geometric deformation. The study introduces a novel synthesis of two independent techniques, namely the zero-complexity factor and density-like constraints, applied simultaneously to determine the deformation functions. This dual implementation represents a new methodological step in stellar modeling, as it allows us to explicitly control the role of anisotropy and complexity in the internal structure of self-gravitating objects. Starting from a chosen metric ansatz as a seed solution, we demonstrate that the zero-complexity condition captures the gravitational response of compact matter in a fully tractable form. The complete deformation procedure then yields two new physically viable anisotropic solutions, passing all standard stability and energy condition tests. Our results show, for the first time, that the direction of energy transfer between the seed sector and the decoupled source is uniquely governed by the deformation parameter, providing direct physical insight into the coupling between known and generic gravitational fields. Furthermore, we find that anisotropy plays a decisive role in the stability criteria of these stars, highlighting its nontrivial influence on realistic stellar evolution. These results offer a new perspective on the modeling of high-density stellar interiors and open a pathway for extending gravitational decoupling analyses to more complex astrophysical scenarios.