Asymptotically flat wormhole solutions with variable equation-of-state parameter

Abstract

This paper discusses exact wormhole solutions in the framework of general relativity with a general equation of state that reduced to a linear equation of state asymptotically. By considering a special shape function, we find classes of solutions which are asymptotically flat. We study the violation of the null energy condition as the main ingredient in wormhole physics. The possibility of finding wormhole solutions with asymptotically different state parameter is investigated. We show that in principle, a wormhole with a vanishing redshift function and the selected shape function, cannot satisfy the null energy condition at a large distance from the wormhole. Our solutions have the positive total amount of matter in the ``volume integral quantifier'' method. For this class of solutions, fluid near the wormhole throat is in the phantom regime which at some $r={r}_{2}$, the phantom regime is connected to a distribution of dark energy regime. Thus, we need a small amount of exotic matter to construct wormhole solutions.