Studies of relativistic rotating stars: numerics and stability tests

We introduce a version of the Spectral Einstein Code that can evolve coupled hydro and spacetime stably for long timescales in 2D axisymmetry. We show code test results that demonstrate long-term numerical stability. As a first application of this code version, we study the turning point criterion. Along a sequence of equilibrium uniformly rotating, isentropic stars, it has been proved that stars on one side of a turning point are secularly unstable. Efforts have been made to establish the applicability of the criterion for differentially rotating stars as well, which are expected to be produced during binary neutron star mergers. We explore the stability of stars with different rotation laws and equations of state with an aim to test how well the criterion holds for more general cases. For this, we investigate sequences of equilibria and evolve them on a dynamical timescale.