Isotropization and New Solutions for Self-Gravitating Systems with Zero Complexity

Abstract

This thesis explores the compact stellar structure in the context of the F(R,LM,T) gravity theory, employing the Minimal Geometric Deformation (MGD) technique via gravitational decoupling (GD). Starting with the isotropic Durgapal-Fuloria (DF) solution, we construct its anisotropic extension and develop two additional models by imposing vanishing and equal complexity factor conditions. The complexity factor, derived from the Riemann ten- sor’s orthogonal decomposition, serves as a key tool to understand the structural intricacies of self-gravitating systems. The physical viability of the models is tested against observa- tional data from the pulsar PSRJ0740 + 6620, using mass and radius constraints obtained from NICER and XMM-Newton observations. A detailed graphical analysis is conducted to study the radial behavior of energy density, pressure components, and anisotropy, and the parameter space ensuring physical viability is summarized in tabular form for each model.