Eigenmodes in a ultrarelativistic pair QED-plasma

Ultra-magnetized neutron stars -- magnetars -- possess surface magnetic fields far in excess of the quantum limit (Schwinger) field. Therefore, various plasma waves propagating through the magnetar magnetosphere filled with relativistic plasma have their dispersion modified by the QED effects. Here we derive the linear modes in ultrarelativistic (non-)neutral ultra-magnetized pair plasma. The results are discussed.