Gravitational Wave Astronomy refers to a new branch of astronomy,
which aims at the detection and analysis of gravitational waves that
reach us from astrophysical sources like black holes, neutron stars,
or supernovae. Such waves are predicted for the dynamics of massive
objects by Einstein's theory of general relativity.
The goal is the development of robust and efficient methods for the
numerical solution of the Einstein equations. Gravitational wave
astronomy requires numerical solutions of high reliability and
accuracy for the theoretical prediction and analysis of gravitational
waves. Focus areas are reformulations of the Einstein equations,
numerical methods for the Einstein evolution problem including
structure preservation, efficient elliptic solvers for adaptive meshes
and black hole geometries, and the adaptation of these numerical
algorithms to wave problems.
A central problem of computational physics is to make the physical
features manifest in the discrete system, e.g. to preserve structure
during a time integration. This is particularly hard in NR,
essentially due to diffeomorphism invariance. Writing the Einstein
equations in the form of an initial value problem, the number of
computational degrees of freedom (DOF) is much larger than the
physical DOF, since it is not known in general how to separate
physical from gauge and constraint violating DOF Due to the
complicated nonlinear structure of the Einstein equations it has not
yet been possible to directly carry over techniques that solve
conceptually related issues in other gauge theories such as the
Maxwell equations. Consequently, numerical relativity simulations are
typically plagued by instabilities, which are often rooted in the
continuum formulation of the problem.
The study of wave emission from compact objects requires resolution at
different scales: a code needs to resolve the compact objects, their
orbits, emitted waves and a slowly varying background. In order to
obtain accurate results both the use of mesh refinement techniques and
a good choice of coordinate gauges is essential. Here the focus of
this project will be on efficient techniques for mesh refinement, in
particular also concerning efficient solvers for elliptic
equations.
For further details see
SFB/Transregio 7
Gravitationswellenastronomie
and the
initial data project.