Insight into Gravitation via a Combination of Analytical and Numerical Methods

• Applicant: Professor Dr. Oliver Rinne
• Subject Area: Mathematics ; Astrophysics and Astronomy ; Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2012 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 215772344

Einstein's field equations of general relativity are notoriously difficult to solve analytically. In many interesting situations one has to resort to numerical methods. This is important not only for the quantitative modelling of astrophysical sources of gravitational radiation but also in order to provide qualitative insight into open questions of the theory. The latter is the goal of this project, based on a rigorous analysis of the underlying equations and the use of highly accurate numerical methods.New methods for constructing entire spacetimes numerically will be developed, all the way out to future null infinity, the asymptotic region that outgoing light rays approach. A main application is the study of gravitational collapse, in particular critical phenomena at the threshold of black hole formation, both in spherical symmetry and in axisymmetry. Other geometric evolution equations such as Ricci flow and their applications to general relativity will also be considered.

• DFG Programme: Research Grants