Study of non-commutative wormhole solutions in f (R, G) gravity

In this paper, we investigate some feasible regions for the existence of wormholes by introducing non-commutative geometry in terms of Gaussian and Lorentzian distributions in f (R, G) modified theory of gravity. We explore wormhole solutions by assuming a viable model f (R, G) = f(1)(R) + f(2)(G), where f(1)(R) is assumed to be a linear function of Ricci scalar and f(2)(G) is chosen to be a power law model. For f (R, G) model under discussion, we select suitable form of redshift and shape functions, which is necessary for the existence of wormholes. We discuss mainly two types of solutions corresponding to different values of free parameters and obtain numerical results. The stability condition for numerical solutions is discussed via TOV equations and it is proved that gravitational and hydrostatic forces show opposite behavior to anisotropic force and hence cancel each other's effect, which provides a stable wormhole configuration. By using graphical evolution, it has been found that null energy conditions (NEC) are violated for non-commutative Gaussian and Lorentzian distributions. However, some feasible regions have been found for the existence of wormhole solutions with Gaussian and Lorentzian distributions in the context of f (R, G) gravity.