Computational methods in gravity and string theory

My research centres on gravity in string theory, where no analytic (ie. pen and paper) methods are available. My aim is to develop practical numerical computer methods to solve these. Combining gravity and quantum mechanics is a key achievement of string theory. From my perspective there are two questions; Firstly, is it `the' theory? Secondly - and independently - what can we learn about, and from, black holes - the fundamental object in gravity? 1) String theory predicts gravity in 10 spacetime dimensions - we only see 4. If extra dimensions have a finite, small volume, observing on larger scales than this volume, they manifest only as extra matter in our 4 (infinite) dimensions. What appears as empty spacetime to us - a `vacuum solution' - is generically a complicated geometry in the extra dimensions. In simple cases these are classified, and called Calabi-Yaus, but are not known explicitly. They obey Einstein's gravity equations, which are too hard to solve analytically as the geometry depends on all 6 extra dimensions. What appear as black holes are even more complicated. Even with only one extra dimension - where at least the vacuum is simple - only one variety of black hole is known analytically. CERN's LHC (turning on in 2007) may even be powerful enough to probe extra dimensions and produce these exotic black holes directly. Understanding the geometry of these extra dimensions and black holes is important if we are to understand the predictions of string theory (for example, the extra matter we might see in 4d due to the extra dimensions) and be able to test it. Part of my work is finding ways to solve Einstein's equations of gravity. I developed computer methods to tackle geometries depending on 2 coordinates - such as the black hole problem for one extra dimension. I tackled more coordinate dependence but focused on a subclass of geometries - called `Kahler', of which Calabi-Yaus are examples, and explicitly demonstrated these for K3 - a 4-d Calabi-Yau. Developing these methods further is an important goal for me, and in particular understanding how to efficiently tackle 6-d Calabi-Yaus which require much computing power. Longer term I aim to develop practical methods to solve Einstein's equations for general geometries, including matter, and depending on many coordinates. My past work hints at the best way to approach this. 2) In specific cases string theory describes identical physics from different viewpoints. One description is gauge theory - similar to QCD - living in fewer than 10 dimensions and having a tunable parameter (`coupling'). For large coupling there is an identical gravity description in 10 dimensions. Thus mysterious quantum gravity is equivalent to a completely well defined gauge theory in fewer dimensions - so called `Holography'. The only catch is the gauge theory is too complicated at large coupling for analytic methods. Gravity allows us to learn about these gauge theories at large coupling. When the gauge theory is confining (just like QCD) using the above numerical methods I constructed exotic new black hole solutions in the gravity description. They are understood as stable balls of hot plasma in the gauge theory - `plasma-balls'. Understanding whether these objects can be used to understand actual QCD behaviour, observable in future heavy ion collider experiments, is an important future direction I will pursue. Gauge theory teaches us about quantum gravity. In the simplest situation the gauge theory is just a quantum mechanics. This has a large number of fields, so is not trivial, but in principle is soluble on a computer. I have recently solved a closely related system - just lacking the `fermions', a particular type of matter. Including these complicates the calculation, and my aim is to extend my methods to this case. If successful I could compute from first principles the quantum properties of black holes.