Construction of anti-de Sitter-like vacuum spacetimes using the conformal Einstein field equations

Diego Carranza (Queen Mary)

RESUMEN: Since Maldacena's work on the AdS/CFT correspondence, study of the adS spacetime has attracted significant attention from different areas of theoretical physics and mathematics. In this context, understanding its conformal boundary is particularly relevant for numerical simulations, as the construction of of these kind of spacetimes depends on the prescribed boundary data. Furthermore, there is numerical evidence that for some class of boundary conditions, this solution is unstable under non-linear perturbations. The problem of the construction of these spacetimes has been addressed by Friedrich as an initial-boundary problem. Although successful, the methods and equations employed are not ideal for numerical implementation. Motivated by this work, in this talk I will explain how the methods of conformal geometry enable us to locally construct solutions to Einstein equations with negative cosmological constant via a system of wave equations for the geometric fields. The talk is based on the recent article Class. Quantum Grav. 35 245006, for which an "insight" piece was selected to be published on the CQG+ blog.