Possibility of traversable wormhole formation in the dark matter halo with istropic pressure

Abstract We explore the possibility of traversable wormhole formation in the dark matter halos. We obtain the exact solutions of the spherical symmetry traversable wormhole with isotropic pressure condition, based on the Navarro–Frenk–White (NFW), Thomas–Fermi (TF) and Pseudo Isothermal (PI) matter density profiles. The derived traversable wormhole solution satisfies the flare-out condition for a specific dark matter center density and equation of state. We extend the spherical symmetry traversable wormhole solutions to an axisymmetric one. The weak energy condition (WEC) and null energy condition (NEC) are then checked near the wormhole throat, and we find that these traversable wormholes violate the WEC and NEC. Our traversable wormhole solutions show that the dark matter at the center of wormhole spacetime will be redistributed by the presence of a traversable wormhole, and the behavior of dark matter density is similar to a black hole spike.