Nonlinear radial oscillations of neutron stars

Abstract: The effects of nonlinear oscillations in compact stars are attracting considerable current interest. In order to study such phenomena in the framework of fully nonlinear general relativity, highly accurate numerical studies are required. We present a numerical scheme specifically tailored for studies, based on formulating the time evolution in terms of deviations from a stationary equilibrium configuration. Using this technique, we investigate nonlinear effects associated with radial oscillations of neutron stars for a wide range of amplitudes. In particular, we discuss mode coupling due to nonlinear interactions, the occurrence of resonance phenomena, shock formation near the stellar surface as well as the capacity of nonlinearities to stabilize perturbatively unstable neutron star models.