Dynamics of some compact structures and moment of inertia in f(ℛ,𝒯 ) gravity

The primary objective of this study is to conduct a thorough examination of relativistic structures within the framework of Formula: see text gravity, where Formula: see text is the Ricci scalar and Formula: see text is the trace of the energy–momentum tensor. We investigate the emerging characteristics of compact stars, focusing on the Formula: see text model, where Formula: see text is the coupling constant. In the initial sections of the paper, we concentrate on the examination of exact interior solutions involving perfect fluid. With this aim, we introduce the metric coefficient Formula: see text, where Formula: see text and Formula: see text are arbitrary constants to be computed from the matching conditions and Formula: see text is a positive odd integer. It is worth noticing that we select a group of 10 significant compact stars from recent studies, namely, Vela Formula: see text, EXO Formula: see text, Formula: see text, SMCFormula: see text, HerFormula: see text, PSR Formula: see text, PSRFormula: see text, CenFormula: see text, Formula: see text and LMCFormula: see text. To investigate the viability of our model, we conduct various checks, including the analysis of energy density and pressure components, equilibrium, and energy conditions, stability analysis and the adiabatic index. An important part of this work provides the slowly rotating property of stars, accompanied by the derivation of the moment of inertia. The relationship of mass, energy density, radius and moment of inertia for stellar objects are observed. Our findings demonstrate that obtained results are physically acceptable and consistent with our considered model.