Project Details
Projekt
Geometrically defined asymptotic coordinates in General Relativity
Subject Area
Mathematics
Term
since 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 441897040
The main objective of this project is to study the relation of geometric, asymptotic foliations of an asymptotically flat manifold to the asymptotic structure itself. Of main interest are physical and geometric invariants such as mass and center of mass. We wish to construct geometrically defined asymptotic "center of mass" coordinate systems to study the condition of being asymptotically flat from a purely invariant point of view. We intend to compare these coordinate systems to other choices of asymptotic coordinate systems, such as harmonic coordinates or CMC-coordinates.The important new aspect is that we consider not only Riemannian manifolds but more generally initial data sets in General Relativity and wish to construct coordinate systems that do not depend on the choice of initial data set in a given spacetime.A further objective is to investigate the Regge--Teitelboim asymptotic parity conditions forasymptotic coordinates in asymptotically flat initial data sets and study their generality with respect to coordinate changes respecting the asymptotic structure. In particular, we are interested in constructing or otherwise proving existence of examples of initial data sets that do not satisfy these conditions in any asymptotically flat coordinate system.We attempt to develop methods that are robust enough to allow being carried over to the asymptotically hyperbolic setting.
DFG Programme
Priority Programmes
Subproject of
SPP 2026:
Geometry at Infinity
