Relativistic fluids interacting through gravitational decoupling in f(T,𝒯) theory

In this paper, we will manifest how polytropic fluids produce effects on an alternate gravitational source, regardless of its features, for spherically symmetric and static spacetimes. For this purpose, we use [Formula: see text] modified gravity, which is characterized by the trace of an energy–momentum tensor as [Formula: see text] and torsion scalar [Formula: see text], Additionally, using the polytropic equation of state, we will speculate about the distribution of energy among fluids within an astrophysical object. We offer a thorough methodology for identifying generic relativistic polytropes accompanied by the minimal geometric decoupling technique. Ultimately, a few tangible attributes of polytropes along with perfect fluids are observed using the Tolman IV solution, including total pressure, energy interchange, and thermal characteristics.