Wormhole solutions with a polynomial equation-of-state and minimal violation of the null energy condition

Abstract This paper discusses wormholes supported by general equation-of-state, resulting in a significant combination of the linear equation-of-state and some other models. Wormhole with a quadratic equation-of-state is studied as a particular example. It is shown that the violation of null energy condition is restricted to some regions in the vicinity of the throat. The combination of barotropic and polytropic equation-of-state has been studied. We consider fluid near the wormhole throat in an exotic regime which at some r=r₁ r=r1, the exotic regime is connected to a distribution of asymptotically dark energy regime with -1-1ω-1/3. We have presented wormhole solutions with small amount of exotic matter. We have shown that using different forms of equation-of-state has a considerable effect on the minimizing violation of the null energy condition. The effect of many parameters such as redshift as detected by a distant observer and energy density at the throat on the r₁ r1 is investigated. The solutions are asymptotically flat and compatible with presently available observational data at the large cosmic scale.