Effects of dark matter on construction of redshift function and new wormhole geometries in de Rham–Gabadadze–Tolley massive gravity

This work investigates the existence of static and spherically symmetric wormhole geometries within the framework of de Rham–Gabadadze–Tolley (dRGT) massive gravity. The presence of stable wormhole geometries is demonstrated using two different dark matter density profiles: Thomas Fermi and the Einasto spike. It is interesting to note that we compute the redshift and shape functions of the wormholes using the density profile, rotational velocity expressions, and field equations and present a new wormhole solution supported by these dark matter profiles. In particular parameter regimes, the solution admits a traversable wormhole structure, wherein the violation of the null energy condition reveals the necessity of exotic matter to sustain the geometry. Moreover, the stability of traversable wormhole solutions is examined using the Tolman–Oppenheimer–Volkoff equation, providing a comprehensive analysis of their equilibrium and structural stability. Also, we represent the spatial geometry of the wormhole models using embedding diagrams.