Wormholes in $f(R,T)=R+λT+λ_1 T^2$ gravity

Abstract: This study explores asymptotically flat wormhole solutions within the framework of $f(R,T)$ gravity. We analyze $f(R,T)$ expressed as $f(R,T)=R+\lambda T+\lambda_1 T^2$. A linear equation of state is employed for both radial and lateral pressures, resulting in a power-law shape function. The investigation encompasses solutions characterized by both negative and positive energy densities. It has been determined that solutions with positive energy density comply with all energy conditions, specifically the null, weak, strong, and dominant energy conditions. Additionally, we identify constraints on the parameters $\lambda$, $\lambda_1$, and the parameters associated with the equation of state and shape function.