Non-commutative wormhole in non-minimal curvature–matter coupling of f(R) gravity with Gaussian and Lorentzian distributions

Abstract

In this work, we construct two new wormhole solutions in the theory dealing with non-minimal coupling between curvature and matter. We take into account an explicitly non-minimal coupling between an arbitrary function of scalar curvature [Formula: see text] and the Lagrangian density of matter. For this purpose, we discuss the Wormhole geometries inspired by non-minimal curvature coupling in [Formula: see text] gravity for linear model in [Formula: see text] as well as nonlinear model in [Formula: see text]. To derive these solutions, we choose the Gaussian and Lorentzian density distributions. To check the viability of these solutions, we plot the graphs for energy conditions and wormhole parameters. It is found that obtained wormhole solutions in both distributions satisfy the energy condition. The resulting wormhole solutions for both non-commutative distributions are determined to be physically stable when we evaluate the stability of these wormhole solutions graphically. It is concluded that wormhole solutions exist with viable physical properties in the non-minimal curvature–matter coupling of [Formula: see text] gravity with Gaussian and Lorentzian distributions.