The amplification of magnetic fields during compact object mergers remains one of the central open questions in high-energy and multi-messenger astrophysics. Observational evidence indicates that binary neutron star (BNS) merger remnants can power short gamma-ray bursts, implying the presence of intense, large-scale magnetic fields—seemingly at odds with the relatively weak fields observed in old double neutron star systems. Yet, the physical mechanisms responsible for generating and sustaining such strong fields remain debated.
In this talk, I will explore the problem of magnetic field amplification with a particular focus on the role of the magneto-rotational instability (MRI). I will highlight recent extensions of the classical MRI framework aimed at bridging the gap between idealised theoretical models and the extreme conditions found in merger simulations. Finally, I will discuss the close connection between magnetic field amplification and the development of turbulence, outlining how recent advances in relativistic turbulence modelling shed new light on this problem.