Are Wormholes predicted by the theory of general relativity? Just like it predicted gravitational time dilation, gravitational lensing. What does it mean to predict something, Does it mean that we'll find wormholes in nature one day?
 A: When people talk about a theory, for example general relativity, they really mean two different things:


*

*the equations that describe the system

*the input parameters
Let me illustrate this with a simple example. Anyone who did physics at school learned Newton's laws of motion, and in the 400 or so years since Newton formulated them the laws have been experimentally tested over and over again. In the low density, low velocity, limit they are essentially a perfect description of how things move.
But suppose we take Newton's second law, and put the mass in as a negative number. Then Newton's second law predicts that if you try and push the object away it moves towards you, and the harder you try and push it away the faster it accelerates towards you. This is obviously nonsense, but does it mean that Newton's laws are wrong? Well no, it means that putting in the mass as a negative number is physically meaningless because mass can't be negative. If you put in meaningless input parameters then you'll get meaningless results, which is a well established principle.
This is what Ben is getting at in his answer. General Relativity does indeed predict wormholes, but only if you use input parameters that are physically meaningless (or at least currently believed to be physically meaningless). In particular all the wormholes I know of require a type of matter called exotic matter, and this is physically meaningless in the same way that a negative mass is physically meaningless.
So the answer to your question is that although GR does indeed predict the existance of wormholes, we will never find wormholes in nature because the conditions needed to create them don't exist.
A: General relativity doesn't have much predictive power unless you assume something about the types of matter that exist. These assumptions are called energy conditions. An example of matter that violated an energy condition would be matter that had negative mass, so that if you dropped it, it would fall up. Another example would be matter in which the speed of sound is greater than the speed of light. Energy conditions are believed to be good descriptions of all actual forms of bulk matter in the universe, but are believed to be false at scales where quantum mechanics is important, and also at cosmological scales where dark energy is important.
Given some energy conditions that we know apply to bulk matter, there is a theorem that says it is impossible to create a wormhole that doesn't already exist, unless the universe already contains closed, timelike curves (CTCs). A CTC would be like a science-fictional "time loop," a place in the universe where you could go and time would repeat rather than going on forever. We have no evidence that CTCs exist in our universe, and if they did, it would raise strange issues about cause and effect.
Based on these facts about the observed universe (no exotic matter, no CTCs), the assumptions of the theorem hold, and it therefore seems pretty clear that wormholes cannot have arisen as a result of natural gravitational collapse, and they cannot be created artificially. If wormholes were created in the big bang, then the theorem doesn't apply, because it's about creating wormholes that didn't already exist.
Even if wormholes did exist, estimates by Ford and Roman show that it's unlikely that you could send a material object through a wormhole without destroying the object. Even information probably can't get through. In other words, a wormhole probably wouldn't be traversible.
If you did have a wormhole, and it was traversible, you could use it to create a time machine. See https://physics.stackexchange.com/a/135670/4552 . As with CTCs, this would create violations of causality, such as being able to go back in time and kill your own grandfather in the cradle.
So in summary, GR gives us very strong reasons to believe that science-fiction-style wormholes do not and cannot exist. However, there is enough wiggle room that one can write a science fiction story about a wormhole without completely violating GR. It's not as completely silly as Star Trek-style warp drive. (The Alcubierre metric is not a Star Trek-style warp drive.)
This FAQ may be helpful: http://www.webfilesuci.org/wormholefaq.html
