Modeling Wormholes Generated by Dark Matter Galactic Halos in f(R)$f(R)$ Modified Gravity

Wormholes (WHs) are hypothetical topologically non-trivial spacetime structures that can be freely traversed by observers and connect two asymptotic regions or infinities. From the current theoretical development, the prospect of their existence is challenging but cannot be excluded. In this paper, generalized Ellis–Bronikov (GEB) traversable WH geometries for static and spherically symmetric spacetime in the background of $f(R)$ gravity is explored. First, the Tsujikawa-like $f(R)$ model and the shape function for the GEB model is considered, which depend on a sequence of simple Lorentzian WHs with two parameters: a free even integer exponent, n, besides the throat radius, r₀. One also consider that these WHs are generated by dark matter galactic halos (DMGHs), based on the three most common phenomenological models, viz., Navarro–Frenk–White (NFW), Thomas–Fermi (TF), and pseudo-isothermal (PI). In this concern, the satisfaction of the energy conditions (ECs) which are dependent on the dark matter (DM) models, viz., dominant energy condition (DEC) and strong energy condition (SEC) and those which are not dependent viz., null energy condition (NEC) and WEC at the WH throat and its neighborhood is investigated. Finally, the presence of exotic matter is confirmed by the violation of the NEC in all cases, revealing the supremacy and physical acceptability to support the existence of the WHs and making them compatible and traversable in Tsujikawa's-like $f(R)$ model.