Traversable wormholes satisfying the Karmarkar condition in f(R) gravity with deflection angle of light

Abstract

In this present work, we introduce a completely new wormhole shape function satisfying the Karmarkar condition that constructs static, spherically symmetric wormhole solutions in the framework of modified $f\left(R\right)$ gravity. The proposed shape function generating wormholes are asymptotically flat by satisfying the essential conditions. Here, we consider two well-known $f\left(R\right)$ gravity models, namely the exponential $f\left(R\right)$ gravity model, and the Tsujikawa $f\left(R\right)$ gravity model, interestingly, the reported shape function generating wormholes are static, and spherically symmetric structures in the circumstances of the non-existence theorem and supported by the non-exotic matter in those $f\left(R\right)$ gravity models corresponding to the suitable values of free parameters. Moreover, the non-exotic matter supporting wormholes are in the equilibrium state by satisfying the ToV-equation in both the considered $f\left(R\right)$ gravity models. We also study the weak gravitational lensing in the spacetime of the present wormhole structures and estimate the deflection angle of light that decreases for increasing values of the impact parameter.