Carla Cederbaum (Tübingen), Oliver Rinne (Golm)
Carla Cederbaum (Tübingen)
Mathematical General Relativity: hypersurfaces of constant time
After a brief introduction into General Relativity, in particular the
Einstein equations, we will concentrate on so-called \emph{initial data
sets}. These are special Riemannian manifolds arising as “hypersurfaces
of constant time” in relativistic spacetimes and solving a system of
geometric elliptic PDEs. We will discuss a selection of questions one
can ask about initial data sets such as “How do you define their mass
and center of mass?” We will also present some geometric uniqueness
results in the more special setting of static spacetimes/initial data
sets.
Oliver Rinne (Golm):
Einstein equations and their numerical solution: hyperboloidal hypersurfaces
This talk will begin with a brief introduction to the Cauchy or initial
value problem in general relativity. It forms the basis for numerical
solutions of the Einstein equations. In asymptotically flat spacetimes,
the question arises how to treat the spatially unbounded domain
numerically. An attractive option is to foliate spacetime into
hyperboloidal (asymptotically characteristic) hypersurfaces, which may
be compactified to include infinity. I will present selected
applications of this scheme involving black hole spacetimes with matter
fields and gravitational radiation.
