Wormhole solutions for different shape functions in 4D Einstein Gauss–Bonnet gravity

Abstract

In this paper, we obtain an exact spherically symmetric wormhole solution with anisotropic matter distribution in the regularized four-dimensional (4D) Einstein Gauss–Bonnet gravity (4D EGB). Recently, a new attempt has been made to include nontrivial contributions of Gauss–Bonnet term to the gravitational dynamics by regularizing EGB gravity in [Formula: see text]-dimensions. To find the exact solution of the wormhole geometry, we studied two specific radial-dependent shape functions [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text] in the context of 4D EGB gravity. For each shape function, we find the exact wormhole solution and analyze the properties of wormhole existence graphically. The anisotropic parameter, equation of state (EoS) and energy conditions are tested graphically for each shape function. The behavior of both shape functions is thoroughly evaluated with the throat radius [Formula: see text]. Specifically, we recovered the original results exactly to 4D Morris–Throne wormholes of General Relativity by simply imposing the limit as [Formula: see text] and comparison has been done between the branch results in 4D EGB gravity and General Relativity by graphical point of view.