Cosmic string time machines

One possible way that Tipler’s time machine could be realized is
by using cosmic string. We saw in the previous chapter how useful
cosmic string would be in keeping a wormhole’s throat open. Yet
again, this might be just the right sort of materialweare looking for.
It would be infinitely long and would certainly be dense enough.
All we would need to do is get it spinning fast enough. This does
of course assume that (a) cosmic strings exist, (b) we are able to
locate and travel to one, (c) we could find some way of spinning it
fast enough and (d) a closed time loop really would form around
it.
Even when a cosmic string is not spinning, spacetime around
it is distorted in a rather strange way (yes, stranger even than
spacetime around a black hole!). Despite the high density of the
string, you would not feel an attractive gravitational force however
close you were to the string, and spacetime is said to be flat.
However, space by itself will be cone-shaped around the string.
To see this, consider 2D space for simplicity and a circular patch
of this space around the string. would be shorter than the distance you would cover round a circle
of the same radius in normal space (away from the string). Note
that the string is depicted by a 0D point in 2D space. It is really
a 1D line in 3D space (which I am unable to show since I cannot
draw a 4D cone!).
A variation on this cosmic string theme was suggested by
Richard Gott in 1991. He provided a way round the requirement
that the cosmic string needs to be spinning. Instead he showed
how two strings moving past each other at high speed would have
the same effect, and a time loop would form around the pair. The
problem here is that the two strings would have to be parallel to
each other as they passed. So even if cosmic string does exist, we
would still have to hope for two strings to just happen to encounter
each other at just the right angle. Gott points out that we need not
wait for two infinitely long strings to pass each other. The same
effect might be achieved if one closed cosmic string, forming a loop,
which was an oval rather than circular (like the shape formed by
a stretched rubber band) were to collapse in such a way that the
two long sections just miss as they fly past each other. Gott himself
has pointed out that any closed time loops that might form around
two pieces of cosmic string that were not infinite in length would
form a black hole and be shielded from the outside by an event
horizon, which would, of course, mean that they could never be
used.
Unfortunately, Gott’s way of achieving a time loop is even
more hare-brained than the other schemes on the market since,
along with all the ifs and buts I have already mentioned, it requires
part of the total mass of the strings to be what is known as
‘imaginary’.2