Possible existence of traversable wormhole in Finsler–Randers geometry

Abstract

In the present article, we have explored the possible existence of a traversable wormhole in the framework of Finsler–Randers (F–R) geometry. In order to achieve this goal, first, we have constructed gravitational field equations for static, spherically symmetric spacetime with anisotropic fluid distribution in F–R geometry. Next, we have written the deduced form of field equations in the background of Morris–Thorne wormhole geometry. To visualize the shape of the wormhole, we have selected exponential shape function b(r)=frac{r}{expleft( eta left( frac{r}{r_{0}} - 1right) right) } with the constant parameter eta and the throat radius r_{0} and depicted two-dimensional and three-dimensional embedding diagrams corresponding to some considered values of eta and r_{0}. Moreover, all essential requirements to build a wormhole shape have been examined for the reported shape function. Next, We have analyzed wormhole configuration for three cases (I, II, III) corresponding to three selected redshift functions. Furthermore, each case is analyzed by dividing it into two models such as (i) Model-1 (for general anisotropic EoS p_{t}=chi p_{r}) and (ii) Model-2 (for linear phantom-like EoS p_{r} + omega rho =0). In each model of three cases, we have verified the validity of the wormhole solution in F–R geometry by considering null, weak, strong and dominant energy conditions. Also, the total amount of averaged NEC-violating matter near the wormhole throat has been analyzed by computing volume integral quantifier.