New traversable wormhole solutions in Einstein Gauss–Bonnet gravity

Abstract

This paper explores the existence of static wormholes in 4-Dimensional Einstein Gauss–Bonnet (4D EGB) gravity. We discuss some possibilities for constructing radial-dependent shape functions via different strategies to develop some non-conventional wormhole geometries by considering anisotropic matter sources. In this regard, we assume a specific form of the equation of state and investigate its effects on Gauss–Bonnet (GB) coupling parameter. Next, we impose a traceless condition on the anisotropic fluid distribution as well as radial-dependent energy density profile to explore wormhole geometries as separate cases. It is seen that the obtained results can be reduced into Morris–Throne wormholes for the zero value of GB-coupled parameter for anisotropic fluid distribution. Furthermore, we scrutinize flaring-out conditions and examine asymptotically flatness constraints for the existence of wormholes. Our analysis shows that the weak energy condition (WEC) is satisfied for a particular range by constraining GB-coupled parameter. We study the dynamics of GB-coupled parameter for both cases [Formula: see text] and [Formula: see text]. It is concluded that wormhole solutions are possible for [Formula: see text] and, in some cases, [Formula: see text]. The active gravitational mass of developed wormholes is calculated and plotted graphically. The wormhole geometry is discussed by plotting 2D and 3D embedding diagrams. In order to analyze the complexity of the system, we have plotted the complexity factor for each wormhole.