Dark matter influences on wormhole stability in de Rham–Gabadadze–Tolley like massive gravity

Abstract The characteristics of wormhole models in the context of the de Rham–Gabadadze–Tolley-like massive gravity theory are examined in this article. Dark matter density profiles of Thomas Fermi and Einasto spike are used to find the wormhole shape functions. By exploiting these formed shape functions, we create a wormhole geometry that connects asymptotically flat regions of spacetime while fulfilling all necessary requirements. Through a comprehensive analytical and graphical investigation, we explore the characteristics of exotic matter in these wormhole structures and examine their material composition within the context of energy conditions. The volume integral quantifier is used to quantify the exotic matter. We also discuss the phenomena of the complexity factor for all wormhole models and conclude that it approaches zero for increasing values of the radial coordinate, indicating the homogeneity of the energy density and the isotropic behavior of the pressure. Moreover, the repulsive nature of these wormhole solutions, a critical characteristic for their possible traversability is revealed by our analysis of the anisotropy parameter.