Modeling the structure and stability of compact stars in f(R,T) gravity using Tolman–Kuchowicz spacetime

In this paper,we investigate the effects of three different [Formula: see text] gravity models — where [Formula: see text] represents the Ricci scalar and [Formula: see text] is the trace of the energy–momentum tensor — on the modeling of anisotropic relativistic stellar structures. We assume a static, spherically symmetric self-gravitating body within the Tolman–Kuchowicz spacetime framework. After selecting an appropriate vacuum solution, we evaluated various constraints to ensure the smooth matching of the exterior and interior geometries at the boundary surface. Using observational data from three well-known stellar structures, Her X-1, SAXJ1808.4-3658, and 4U1820-30, we examined the viability of energy conditions under quadratic, cubic, and exponential [Formula: see text] models. We analyzed energy density distributions, anisotropic pressure behavior, and the roles of fundamental gravitational forces, along with stability assessments through realistic plots of compact star models. Our findings indicate that modified gravity theories can be considered a viable tool for studying the existence and properties of compact stellar structures at both theoretical and cosmological scales.