Stellar configurations in <i>f</i> ( <i>R</i> , <i>L</i> _<i>m</i> , <i>T</i> ) gravity: probing anisotropy and stability via minimal geometric deformation

Abstract This study uses a minimal geometric deformation scheme within the gravity paradigm to model anisotropic compact stars using class-1 embedding spacetime. We introduce the deformation of the radial component of the metric tensor, which decouples the Einstein field equations and introduces an additional gravitational source. The relevant constants are evaluated using observational data from seven realistic star candidates by matching the inner region with the outer Schwarzschild line element. A comprehensive graphical analysis of three compact stars is performed to examine the impact of the coupling parameter β and deformation parameter n , revealing positive, well-behaved energy densities and pressures that satisfy the energy conditions. The study found that negative values of the coupling parameter β allow greater mass accumulation while preserving key physical characteristics, such as stability under Herrera's cracking condition and the extended Tolman-Oppenheimer-Volkoff equation. This study highlights the significance of gravitational decoupling for determining mass, redshift, and compactness and provides important insights into the internal structure of stellar bodies within this new generalized gravity framework.