Anisotropic extensions of Tolman IV through decoupling in energy–momentum squared gravity

Abstract

This paper is dedicated to the precise computation of anisotropic extensions for the Tolman IV solution. These extensions are achieved through the utilization of the extended gravitational decoupling scheme within the framework of [Formula: see text] gravity, where R is the Ricci scalar and [Formula: see text] is the contraction of energy–momentum tensor. In this context, we select a linear model characterized by the expression [Formula: see text], where the parameter [Formula: see text] establishes a connection between the geometric and matter components. The extended gravitational decoupling technique incorporates a decoupling parameter that governs the extent of the induced anisotropy. Deformations in the radial and temporal metric components lead to the decomposition of the field equations into two distinct subsystems. One of these sets pertains to the isotropic solution, while the other is addressed by implementing the extra constraints. We examine the outcomes through graphical analysis and investigate the viability and stability of the obtained anisotropic solutions for the celestial object. Moreover, we study the mass, compactness and surface redshift of the system to gain a comprehensive understanding of its characteristics. It is concluded that this technique in this modified gravity yields physically acceptable solutions.