In the realm of science fiction, one common theme seems to be a capability to somehow by some loophole travel faster than the speed of light. Some theoretical physicists are taking note and examining some solutions and noting that under some conditions, they might be plausible. One convenient loophole which Einstein introduced in 1955 was the idea of the wormhole. A wormhole would essentially be a tear in the fabric of space that would allow one to traverse it in order to get to the other side of the tear, similar in idea to the representation in the picture above. The catch for being able to traverse a wormhole, which would actually exist inside a black hole, would be to have something called negative matter, which may or may not exist. Theoretically, negative matter would be lighter than nothing, and would allow one to keep open a wormhole. The required amount of negative mass however for even a one meter wormhole would essentially be a negative Jupiter of mass, which given current and even future technology, seems a distant possibility indeed.
One of the most well known ideas of faster than light travel in modern culture is the ability to go to warp, which gained enormous popularity in the context of Star Trek. Going to warp means that one is capable of expanding the space behind them, and shrinking the space in front of them such that they can use conventional means of propulsion to move the shortened distance to their destination, andeffectively traveling faster than the speed of light. The ship would travel in a veritable bubble of normal space, such that time passes relative to their origin, such that one would not experience the negative effects of relativity. The catch for such technology however relies on the possibility of such a thing as negative matter existing. Like the concept of wormhole travel, its not yet clear whether this method of transportation is impossible yet or not.
The following excerpt from renowned theoretical physicist Michio Kaku's book, "Physics of the Impossible" explains more about the applications of Einstein's general theory of relativity.
Physics of the Impossible Excerpt