The main aim of the project is to get a better understanding of gravity as described by Einstein's theory of general relativity (GR). In the past, applications to astrophysics and cosmology motivated by the prospect of detecting gravitational waves were the main driving force in the field. In recent years, GR has led to many developments in areas of theoretical and mathematical physics beyond its traditional playground of astrophysics and cosmology. The main reason for this is the so called the AdS/CFT correspondence, also known as the gauge/string duality. This is a conjectured equivalence between certain string theories (and hence quantum gravity) in (d+1)-dimensional asymptotically anti-de Sitter space (AdS) and certain d-dimensional gauge theories, similar to real world theories of particles. In the regime in which these string theories reduce to classical GR in AdS spaces, the dual gauge theory becomes strongly interacting. Therefore, by studying classical GR in higher dimensional asymptotically AdS spaces we can access, from first principles and in a controlled manner, the strongly interacting regime of certain gauge theories. This is particularly relevant and useful to study far-from-equilibrium processes in such theories because traditional methods in quantum field theory do not work. This has found many applications outside the boundaries of gravitational physics; in particular to high energy physics, in condensed matter physics and more recently in fluid mechanics.
It turns out that GR beyond the astrophysical setting is poorly understood. For instance, black holes can have new shapes and they may suffer from dynamical instabilities whose endpoints are not known. Moreover, gravity in AdS space exhibits new phenomena, which are not present in the astrophysical context, and which often arise in the full non-linear regime of the theory. Hence numerical methods are the only tool available to study them. The main aim of this project is to get a better understanding of gravity, as described by GR, in scenarios that naturally arise in the context of the AdS/CFT correspondence, namely higher dimensional and/or AdS spaces, using numerical methods. This project has two general objectives:
1) Develop new numerical codes to study time-dependent spaces.
2) Find new types of equilibrium black holes.
