On possible traversable wormhole solutions supported by Karmarkar condition in R2−gravity within the f(R,T)−formalism

In their seminal work, Morris and Thorne (1988) introduced the concept of traversable wormholes (WHs), which are geometric structures serving as bridges to connect two distinct spacetimes or different points within the same spacetime. The properties of these WHs are determined by the choice of the shape function. Extensive research has been conducted in the literature on WHs within modified theories of gravity, considering various types of shape functions. In this paper, we focus on deriving the simplest solutions for traversable WHs within the framework of $f(R,T)$ gravity. Our specific focus lies on the functional form $f(R,T)=R+\alpha R^2+\lambda T$, where $R$ represents the Ricci scalar and $T$ denotes the trace of the energy–momentum tensor. By incorporating quadratic geometric and linear material corrections, we demonstrate that the matter content of WHs can obediently conform to the energy conditions (ECs). This study significantly advances our understanding of WHs within the context of modified gravity. Our findings shed new light on the behavior and properties of WHs, highlighting their compatibility with the $f(R,T)$ gravity framework. By unveiling the ability of WHs to adhere to ECs through the inclusion of geometric and material corrections, we provide groundbreaking insights into these intriguing objects. Overall, our research contributes to the broader field of gravitational physics by presenting a unique perspective on WH modeling. By exploring WHs within the $f(R,T)$ gravity framework and demonstrating their conformity to ECs, we expand our knowledge of these fascinating structures and pave the way for further investigations in this area.