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.