Answer 1:
The Godel Metric is a solution of Einstein's
Equation that has swirling dust particles
(representing galaxies) and a cosmological
constant, which is a parameter that can be tuned
make the universe expand, contract, or stay
stable. One interesting thing about the Godel
Metric is that it allows the existence of closed
timelike curves. Closed timelike curves in the
space time of General Relativity are paths that
allow an observer to start at a certain time,
travel along this path and end up at the same time
she started at! These paths can be further
extended to allow the possibly of traveling back
in time. One other such solution of
Einstein's Equation that allows the existence of
closed timelike curves is the Kerr vacuum, which
models a rotating uncharged black hole. The Kerr
vacuum has closed timelike curves within the
event horizon of the black hole. However, it
is important to note that although these solutions
exist in theory, scientists do not believe that
they exist in reality, and time travel will stay
the topic of science fiction. The Godel Metric,
as well as most other solutions of Einstein's
Equation that allow closed timelike curves, are
only mathematical toy models that do not exist in
nature. The Kerr metric mentioned above is
thought to be a good representation of the real
space time around a rotating black hole. However,
the closed timelike curves found in the Kerr
solution are only found inside the event horizon
of the black hole, where we unfortunately cannot
travel. Additionally, even though closed timelike
curves exist in the Kerr metric, it is thought
that these are just artifacts left over because
General Relativity does not take quantum mechanics
into account. A full quantum theory of gravity
will most likely not contain closed timelike
curves, as we cannot have them exist in
reality. So, although General Relativity has
solutions that suggest time travel would be
possible, these are merely mathematical
curiosities, and any theory must always pass a
"common sense" test, and unfortunately commonsense
tells us that time travel is not physically
possible.
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