Role of complexity on the minimal deformation of black holes

Abstract

We investigate spherically symmetric classes of anisotropic
solutions within the realm of a schematic gravitational decoupling scheme, primarily decoupling through minimal geometric
deformation, applied to non-rotating, ultra-compact,
self-gravitational fluid distributions. In this respect, we employ
the minimal complexity factor scheme
to generate physically realistic models for
anisotropic matter distributions, using a well-behaved model. The zero-complexity factor condition enables us to
determine the deformation function for solving the decoupled system.
We explore all the structure-defining scalar variables, such as
density inhomogeneity, strong energy
condition, density homogeneity, and the complexity factor (an alloy of
density inhomogeneity and pressure anisotropy) for the decoupling
constant ranging between $0$ and $1$. We observe that the anisotropy vanishes when the coupling constant is set to unity. This finding holds significance as it implies that, in the context of a zero-complexity factor approach, an anisotropic matter distribution becomes perfect without requiring any isotropy requirements. This work effectively explored the impact of complexity on the composition of self-gravitational stellar distributions. This effective approach enables the development of new, physically realistic isotropic stellar models for anisotropic matter distributions. Additionally, our findings indicate that the complexity factor in static, spherically symmetric self-gravitational objects can significantly affect the nature of the matter distribution within these systems. It is concluded that the minimally deformed Durgapal-IV model features an increasing pressure profile, and the local anisotropy of pressure vanishes throughout the model under complexity-free conditions.