During my PhD I have developed numerical applications for solving PDEs describing black hole spacetimes. These applications are based on a spectral approach in the angular section combined with a finite difference scheme in the complementing part.
Alternative formulations of the gravitational constraints
Every numerical simulation first needs a meaningful initial data. Just as in case of Maxwell’s equations our choices regarding initial data are constrained by the field equations. Because of the nonlinear nature of gravity it is hard to produce a solution with clear physical interpretation.
As gravitational wave detectors continually improve in sensitivity we also have to improve our understanding of the physical content in the initial data. We contribute to this effort by studying the new evolutionary formulation of the constraints.
Linear radiative perturbations around Kerr black holes
Rotating black holes far away from any other objects are best described by the Kerr solution. Its significance is clear if we consider how many astrophysical fenomena is explained by various effects related to this model.
Despite of its importance there are a lot of open questions regarding the Kerr metric.
For more details on these projects follow this link…
and if you are interested in the documentation of our codes follow this one.