Spacelike Geodesics and Other Puzzles in the Mixmaster Universe

Abstract

In this thesis we are going to investigate the behaviour of geodesics in a metric with a singularity known as the ``Mixmaster Universe''. This was motivated from previous work done, where the now well-known AdS/CFT correspondence was used to extract information about an AdS Schwarzschild black hole singularity beyond the horizon by studying correlators on the boundary that correspond to spacelike geodesics which bounce off the singularity. It was then shown that when the singularity was a cosmological one (in this case a Friedmann Robertson Walker cosmology with a Big Crunch), this was no longer possible as it is impossible for spacelike geodesics to bounce off this kind of singularity. This raises the question of whether, when an example of a more general singularity (the ``Mixmaster Universe'') is considered, it is possible for the spacelike geodesics to bounce away from this kind of singularity. This would enable us to potentially extract information about the singularity from the boundary correlators.
Unfortunately, it will be shown that bouncing of such geodesics is extremely unlikely (if not impossible) and thus we would be unable to extract information about the singularity in the mixmaster universe using such a technique. We also discuss another aspect of the evolution of the mixmaster universe which shows that it does indeed have a very complicated evolution.