Creation and dissipation of magnetic fields in non-ideal GRMHD simulations

Compact objects, such as neutron stars and black holes, are characterized by the presence of strong magnetic fields that are crucial to explain the high-energy emission from these sources. Such magnetic fields may be subject to complex evolution inside the hosting relativistic plasmas, like dynamo-like processes amplifying initial seed fields in accretion disks or in the early stages of neutron star formation, or dissipative reconnection events in thin current sheets, as believed to occur in the magnetospheres of magnetars. Here we present a unified treatment of these non-ideal effects within the framework of general relativistic magnetohydrodynamics (GRMHD). Results of recent numerical simulations obtained with the ECHO code will be briefly discussed for selected test cases.