Why are wormholes theoretically possible in general relativity?

[CookieSalesman]

What's the rationale for wormholes??
Aside from being a cool concept, how did someone decide that they were possible? One thing I know is with the space-time concept, where a u-shaped space-time fabric can be connected to, but that suggests the ability to bend spacetime in a ridiculous direction or something doesn't it?

 

[ShayanJ]

The reason is that they are solutions to Einstein Field Equations so they don't conflict with our theories. So we say they may exist.
And about the shape of that bending, people may show you some pictures but I think its better to accept that we can't imagine such things.
How a mind, used to think in terms of a three dimensional Euclidean manifold which is evolving in time, can imagine a four dimensional Pseudo-Riemannian manifold with all crazy kinds of metrics and curvatures?
The answer is: it can't. Our only connection to these things is through mathematics.