In this project we study geometrically defined asymptotic foliations of initial data sets in General Relativity. They allow the
construction of asymptotic coordinate systems which are well adapted to the study of physical invariants such as mass and the center of mass. The type of foliations under consideration includes surfaces of constant mean curvature, constant expansion, and constant spacetime mean curvature.
The main goals of this project are:
- Compare the different foliations and their related coordinate systems. Of particular interest is the influence of the value of physical invariants on the shape and position of the surfaces.
- Of particular interest is to find coordinate systems that do not depend on the choice of initial data sets for a given space-time. This could in particular lead to coordinate independent versions of the Regge-Teitelboim asymptotic parity conditions.
- Do all of the above this with as general asymptotic conditions as possible.
Alejandro Peñuela Diaz
Olivia Vičánek Martínez