Two different shape functions for wormholes in f(R) theory with non-commutative geometry and Lorentzian distribution

Abstract

In this work, the solutions of traversable wormholes are investigated inside modified [Formula: see text] gravity under non-commutative geometry since matter possesses Lorentzian density distribution of a particle-like gravitation source. To find the exact wormhole solutions, two different shape functions [Formula: see text], [Formula: see text], and [Formula: see text], [Formula: see text], are considered. The first shape function was proposed by Mishra and Sharma [A new shape function for wormholes in [Formula: see text] gravity and General Relativity, preprint (2020), arXiv:2003.00298v1 [physics.gen-ph]], however the second is newly defined in this paper. The behaviors of both shape functions are analyzed with the throat radius [Formula: see text]. The equation-of-state (EoS) parameter energy conditions, and anisotropy parameter are discussed with graphical point of view.