This post is about something that almost certainly doesn't exist and what it would be like if it did.
The things in question are Cosmic strings. These are not to be confused with the superstrings of string theory (which are generally sub-atomically tiny). Cosmic strings are very big things and you would know if you had one in your back yard.
If you have a bunch of objects (be they atoms or grains of sand or planets or black holes) and you put them in a row far out in deep space, gravity will eventually pull them all together. But suppose you had an infinite number of such objects and you were somehow able to put them into an infinitely long row. There is no way for gravity to pull them together because there is no center of gravity to pull them into - each object is pulled up by all the objects above it and equally down by all the objects below it.
Even so, tiny irregularities in the spacing of the objects in such a string would tend to cause them to condense out into increasingly large (and widely spaced) lumps like droplets of water on a dew-laden spider's web. But what if the string is perfectly homogeneous? Then there is no way for such irregularities to creep in and the structure is completely stable. This is something like what a cosmic string would be like.
It was thought (before a better explanation came along) that such strings could have formed very early on in the development of the universe (as "topological defects"). Such strings would be very dense - about the mass of Earth for each mile in length, but thinner than a proton. So they would be sort of like black holes stretched out along an infinite line instead of confined to a particular point. But despite all this mass, they would not cause a gravitational force. Instead, their effect on space-time would a bizarre and subtle one. Suppose you took a circular walk around a cosmic string, facing it all the time. When you got back to where you started you'd think you would have turned through 360 degrees, but due to its weird effect on the surrounding geometry, you would actually have found that you would have turned through slighty less than that. Circles only have about 350 degrees instead of the usual 360 when they encircle a cosmic string.
Cosmic strings could also be used as a time machine. If you were to have two parallel cosmic strings passing close to each other at very high speed and you move around and between them in just the right way you could theoretically go back in time. Unfortunately (or perhaps fortunately), this isn't very practical for going back to last thursday week and warning your earlier self that it would probably be better for all concerned if he/she/you didn't get out of bed that day (one of the most common reasons for wanting to travel through time).