Existence of stable wormholes on a non-commutative-geometric background in modified gravity

In this paper, we discuss spherically symmetric wormhole solutions in f(R, T) modified theory of gravity by introducing well-known non-commutative geometry in terms of Gaussian and Lorentzian distributions of string theory. For analytic discussion, we consider an interesting model of f(R, T) gravity defined by $$f(R,T)=f_{1}(R)+\lambda T$$ . By taking two different choices for the function $$f_{1}(R)$$ , that is, $$f_{1}(R)=R$$ and $$f_{1}(R)=R+\alpha R^{2}+\gamma R^{n}$$ , we discuss the possible existence of wormhole solutions. In the presence of non-commutative Gaussian and Lorentzian distributions, we get exact and numerical solutions for both these models. By taking appropriate values of the free parameters, we discuss different properties of these wormhole models analytically and graphically. Further, using an equilibrium condition, it is found that these solutions are stable. Also, we discuss the phenomenon of gravitational lensing for the exact wormhole model and it is found that the deflection angle diverges at the wormhole throat.

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