A survey of recent studies concerning the extreme properties of Morris-Thorne wormholes

It has been known for a long time that Morris-Thorne wormholes can only be held open by violating the null energy condition, which can be expressed in the form $\tau-\rho c^2>0$, where $\tau$ is the radial tension. Matter that violates this condition is usually referred to as "exotic." For any wormhole having a moderately-sized throat, the radial tension is equal to that at the center of a massive neutron star. Attributing this outcome to exotic matter seems reasonable enough, but it ignores the fact that exotic matter was introduced for a completely different reason. Moreover, its problematical nature suggests that the amount of exotic matter be held to a minimum, but this would make the high radial tension harder to explain. If the amount is infinitely small, this explanation breaks down entirely. By invoking $f(R)$ modified gravity, the need for exotic matter at the throat could actually be eliminated, but the negation of the above condition, i.e., $\tau <\rho c^2$, shows that we have not necessarily eliminated the high radial tension. This survey discusses various ways to account for the high radial tension and, in some cases, the possible origin of exotic matter. We conclude with some comments on a possible multiply-connected Universe.