Construction of wormhole under embedded approach through dark matter halos in F(T,TG) gravity

Abstract

In this study, we explore generalized Ellis–Bronnikov and embedded wormhole solutions within the context of $F(T,T_G)$ gravity with an anisotropic matter source. To achieve the necessary conditions for wormhole formation, we investigate the energy conditions within $F(T,T_G)$ gravity. Our analysis includes various matter distributions, particularly dark matter halos, using observational data from the $M87$ galaxy. We also explore the results in the framework of $F(T,T_G)$ gravity, considering three different dark matter halo distributions. For each case, the violation of energy conditions proves the presence of strange matter, say exotic matter, which is a necessary condition for wormhole existence in this gravitational model when dark matter halos are present. We investigate the effect of physical parameters on the stable configurations of the generated thin-shell surrounding the wormhole structure. In the first scenario, we can see that the shape function parameters have a significant impact on the shell’s stable regions. In addition, the considered black hole contributes significantly to the shell’s stability.