The Tipler time machine

By the 1960s and ’70s many more theoretical models of spacetimes
that contained time loops were discovered by a number of
physicists who were studying the properties of the equations of
general relativity. All these models had one thing in common.
They involved rotating massive objects that twist spacetime
around them. The best known work along these lines was due to a young American by the name of Frank Tipler who published
a paper in 1974 which caused quite a stir at the time. Tipler had reanalysed
the work of van Stockum involving a rotating cylinder,
and took it a step further. First he proved mathematically that,
to be sure of a closed time loop around the cylinder, the cylinder
did indeed have to be infinitely long, made of very dense matter
and spin at a rate of thousands of times per second. The biggest
problem was, of course, the ‘infinitely long’ bit, which is easier
said than done. So Tipler then went on to calculate what would be
needed to build a time machine in practice. He suggested that
we might be able to get away with having a cylinder just 100
kilometres long and 10 kilometres wide. The problem was that
he could no longer rely on the mathematics to prove that this
would be sufficient to warp spacetime enough. And even if a
closed time loop could be achieved, the cylinder would have to be
fantastically strong and rigid so as to avoid being squashed down
along its length due to the enormous gravitational strain it would
be feeling. At the same time, it would have to be strong enough to
hold together and withstand the enormous centrifugal force trying
to fling its matter outwards as it spun at a surface speed of over half
that of light. However, he pointed out that these were all practical
problems and, anyway, who knows what might be technologically
possible in the distant future.
To use a Tipler cylinder time machine, you would leave the
Earth in a spaceship and travel to where the cylinder is spinning
in space. When you are close enough to the surface of the cylinder
(where spacetime is most warped), you would orbit around it a
few times then return to Earth, arriving back in the past. How far
back depends on the number of orbits you made. Even though
you feel your own time moving forward as normal while you are
orbiting the cylinder, outside the warped region you would be
moving steadily into the past. This would be like climbing up a
spiral staircase only to find that with each full circle climbed you
are on a floor below the previous one!
A number of other researchers have also suggested that we
may not need infinitely long cylinders to get time loops, and that
time travel may even be achieved by orbiting round a spinning neutron star or black hole, provided they were spinning fast
enough. Astronomers have already found neutron stars (pulsars)
that spin close to the required rate. These are known as millisecond
pulsars because their rate of spin is once every few milliseconds (a
millisecond being one thousandth of a second). Some claim that
we need to simulate a long cylinder, in which case we would need
to pile a number of such millisecond pulsars on top of each other,
then find awayof preventing them fromsquashingdowninto each
other and forming a black hole1. Other calculations imply that
just one rapidly spinning black hole which has shed its horizons,
leaving behind a naked ring singularity, is sufficient to provide a
closed time loop around it. However, the mathematics for all these
wild and wonderful suggestions is far from conclusive.