Initial-boundary value problems in asymptotically anti-de Sitter spacetimes and the AdS/CFT correspondence

The AdS/CFT correspondence relates gravitational theories in an asymptotically Anti-de Sitter (AAdS) spacetime to a quantum field theory (QFT) on its boundary.
In particular, by solving a classical gravitational problem in the bulk, one can obtain predictions for the behavior of the dual QFT at strong coupling. One of the successes of this approach is to model the thermalisation and subsequent evolution of a strongly coupled plasma, where the thermalisation corresponds to forming a black hole in the bulk, and the equations of dissipative relativistic hydrodynamics can be obtained in a formal expansion in derivatives in the boundary directions.

Although there is some literature on numerical relativity simulation in the context of the AdS/CFT correspondence, a systematic complete analysis is still lacking. In this research project we aim to provide a formulation of the initial-boundary problem in as general a manner as possible and then to apply the results to problems relevant for AdS/CFT. In particular, the project would involve:

- studying the initial-boundary value problem for asymptotically locally anti-de Sitter spacetimes. For these spacetimes the general asymptotic structure has been understood analytically and here this information would be used to set up the general initial-boundary value problem. This would firstly be done for pure gravity and then generalized to include matter fields.

- studying the use of harmonic and ingoing null coordinates in this context.

- developing a numerical implementation for examples of interest in the context of the AdS/CFT correspondence.

The detailed research plan will be developed together with the successful candidate, building on his/her previous experience and interests. In particular, it could have a numerical component.

Students applying for this project should have a good knowledge of mathematics and theoretical physics.