Julien Cortier - "On the center of mass for asymptotically hyperbolic initial data sets"
In general relativity, one can describe isolated gravitational systems by 3-manifolds carrying geometric data induced from an embedding in asymptotically Minkowskian spacetimes. There are various ways to assign "global charges" to them as in special relativity, such as energy-momentum, center of mass and angular momentum.
In the case of a negative cosmological constant, it is natural to consider rather asymptotically hyperbolic 3-manifolds. I will describe a recent work with Carla Cederbaum and Anna Sakovich in which we define the center of mass for such initial data sets. It relies on the properties of foliations of a neighborhood of infinity by constant mean curvature surfaces.
