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 nonaxisymmetric 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 nonaxisymmetric modes of compact objects with rotation rates up to the Kepler limit.