Stable anisotropic solutions for compact stars in matter-geometry coupled theory under some specific spacetimes

Abstract This article examines how compact astronomical objects behave under the theoretical framework of f (R, Lₘ, T) f (R, L m, T) theory of gravity. We develop modified field equations by taking into consideration the static internal spacetime which is filled with the anisotropic fluid content. Applying two particular constraints related to the anisotropic pressure and radial metric function allows us to identify two new solutions to these gravitational equations. We obtain differential equations for both models, the integration of which yields constants that are established using matching criteria. The necessity for radial pressure to vanish at the hypersurface is also used to find these constants. Afterwards, for various values of the parameters involved in the considered modified model, we visually assess certain requirements whose fulfillment guarantees the viability of the model. For this purpose, we consider the observational data of a compact star 4U 1820-30. We deduce that both of our models meet the necessary stability and viability requirements. Notably, our study advances the understanding of compact stellar models by demonstrating how the considered theory of gravity modifies their evolutionary pattern compared to general relativity, and provides a robust framework for exploring matter-geometry coupling in future astrophysical research.