Covariant and 3 + 1 equations for dynamo-chiral general relativistic magnetohydrodynamics

The exponential amplification of initial seed magnetic fields in relativistic plasmas is a very important topic in astrophysics, from the conditions in the early Universe to the interior of neutron stars. While dynamo action in a turbulent plasma is often invoked, in the last years a novel mechanism of quantum origin has gained increasingly more attention, namely the chiral magnetic effect (CME). This has been recognized in semi-metals, and it is most likely at work in the quark–gluon plasma formed in heavy-ion collision experiments, where the highest magnetic fields in nature, up to B ∼ 10^18 G, are produced. This effect is expected to survive even at large hydrodynamical/magnetohydrodynamic (MHD) scales, and it is based on the chiral anomaly due to an imbalance between left- and right-handed relativistic fermions in the constituent plasma. Such imbalance leads to an electric current parallel to an external magnetic field, which is precisely the same mechanism of an α-dynamo action in classical MHD. Here, we extend the close parallelism between the chiral and the dynamo effects to relativistic plasmas, and we propose a unified, fully covariant formulation of the generalized Ohm’s law. Moreover, we derive for the first time the 3 + 1 general relativistic MHD equations for a chiral plasma both in flat and curved space–times, in view of numerical investigation of the CME in compact objects, especially magnetars, or of the interplay among the non-ideal magnetic effects of dynamo, the CME and reconnection.