Hypersurfaces in relativistic space-times

08. Februar 2017, 15:00  –  Haus 9, Raum 2.22
Institutskolloquium

Carla Cederbaum (Tübingen), Oliver Rinne (Golm)

  • 15:00 Carla Cederbaum 
  • 16:00 Kaffeepause
  • 16:30 Oliver Rinne 

 

 

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.

 

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