Investigating novel wormhole models in extended teleparallel gravity through thin-shell composed with dark energies

Abstract

This study focuses on the construction of static spherically symmetrical wormhole solutions within the framework of extended teleparallel gravity. To accomplish this, we consider the anisotropic fluid configuration satisfying the barotropic relation between the energy density and radial/tangential pressure and obtain two shape functions. For both functions, the necessary conditions to describe the existence of a wormhole geometry and the energy constraints are found to be satisfied, indicating the presence of a traversable wormhole in the vicinity of curvature-matter coupled gravity. To establish thin-shell around the wormhole geometry, we employ a cut-and-paste methodology with the Schwarzschild black hole as the outer manifold. We also explore the stability analysis of the thin-shell via linearized radial perturbations around the equilibrium shell radius for both shape functions. We study the impact of quintessence, phantom and dark energies on the dynamical configuration of thin-shell around developed wormhole structures. This study concludes that thin-shell shows maximum stability for the second choice of the shape function composed of phantom energy for massive black holes.