Geometriska folieringar och konserverade kvantiteter i matematisk allmän relativitetsteori

Tidsperiod: 2017-01-01 till 2020-12-31

Projektledare: Anna Sakovich

Finansiär: Vetenskapsrådet

Bidragstyp: Bidrag för anställning eller stipendier

Budget: 3 200 000 SEK

Conserved quantities are important in various areas of physics, as in many cases they provide an essential characterization of a physical system. However, to define the mass, center of mass, angular and linear momenta of an isolated system in general relativity is a difficult problem.Geometric models for isolated systems are asymptotically Euclidean hypersurfaces of asymptotically flat spacetimes. Traditional Hamiltonian notions of conserved quantities are coordinate dependent and therefore not very satisfactory. An alternative geometric approach using constant mean curvature foliations overcomes the issue of coordinate dependence, but is restricted to hypersurfaces with small extrinsic curvature. At the same time, conserved quantities derived within the framework of a novel quasilocal approach are hard to compute explicitly. The goal of this project is to develop transparent, coordinate-free notions of center of mass and angular momentum for isolated systems with general asymptotics. For this purpose we propose to consider a new geometric foliation which adequately captures the extrinsic curvature of an asymptotically Euclidean hypersurface. To prove the existence and uniqueness of this foliation, and to study the properties of its leaves we will rely on methods of geometric analysis. With this research we hope to provide important insights into geometry and physics of spacetimes. We also believe that the new definitions will be well-suited for numerical simulations.