In 1999, Lisa Randall and Raman Sundrum proposed a gravitational model where our four-dimensional universe was confined to a brane, which sat at an orbifold point of five-dimensional anti de-Sitter space. At the other end of the orbifold was another brane. This had the somewhat amazing effect that the Planck scale, the gravitational scale felt in our universe, was related to a five-dimensional scale by an exponential quantity, which allowed for the hierarchy problem to be "solved". Furthermore, it turned out that four-dimensional Einstein gravity was recovered on the brane. The last neat feature of this model was that it had the possibility that dark matter could reside on the other brane, which meant that interaction cross sections between normal matter and dark matter would be naturally small. You can see that this model had a number of things going for it!

Alas, it was a little too good to be true. It turns out that the basic model had a very light scalar field which mediated long range forces. To this end, we set about generalising upon the model, to try and understand if this constraint could be alleviated through the introduction of more branes. We considered a model of multiple branes floating in five-dimensional space, and investigated the gravitational behavior of the system. In particular, we looked at a low energy regime, in which a four-dimensional effective theory could be constructed. Our first paper addresses what the four-dimensional theory looks like.

In our second paper, we analyse the physics of the four-dimensional effective theory, and place constraints on it, both theoretical and observational. Unfortunately, we found that our model couldn't get around any of the shortcomings of the original Randall-Sundrum model, and also wasn't helpful for dark matter sequestration. Regardless, it was a fun project to explore.

I would like to come back to five-dimensional models one day, and ask the question of "How do you embed a black hole on a brane?" This was my original motivating question, but it turns out to be a rather difficult problem, and one that many people have attempted to tackle. Recently, it appears that people have succeeded in doing so numerically, but I would still like to contribute something to the problem.