Rotational & magnetic field instabilities in neutron stars

In this short review we present recent results on the dynamics of neutron stars and their magnetic fields. We discuss the progress that has been made, during the last 5 years, in understanding the rotational instabilities with emphasis to the one due to the f-mode, the possibility of using gravitational wave detection in constraining the parameters of neutron stars and revealing the equation of state as well as the detectability of gravitational waves produced during the unstable phase of a neutron star’s life. In addition we discuss the dynamics of extremely strong magnetic fields observed in a class of neutron stars (magnetars). Magnetic fields of that strength are responsible for highly energetic phenomena (giant flares) and we demonstrate that the analysis of the emitted electromagnetic radiation can lead in constraining the parameters of neutron stars. Furthermore, we present our results from the study of such violent phenomena in association with the emission of gravitational radiation.