Dynamics of fast rotating neutron stars: An approach in the Hilbert gauge

We describe a set of time evolution equations and its numerical implementation for the investigation of non-axisymmetric oscillations of rapidly rotating compact objects in full General Relativity, taking into account the contribution of a dynamic spacetime. We derive the perturbation equations for the spacetime in the Hilbert gauge, while the hydrodynamical evolution is based on perturbations of the energy-momentum tensor. In our numerical implementation, we use Kreiss-Oliger dissipation in order to achieve a stable time evolution. Our code features high accuracy at comparably low computational expense and we are able to extract the frequencies of non-axisymmetric modes of compact objects with rotation rates up to the Kepler limit.