The Characteristic Problem in Ideal GRMHD

We consider the characteristic problem in ideal general relativistic magnetohydrodynamics. Combining the fluid and Maxwell equations, we have verified the characteristic equation their wave speeds. We provide corrections to a previous calculation of the eigenvector and its wave speeds. Having calculated all the left and right eigenvectors, we are now in a position to be able to explore the variety of motions within relativistic charged fluids. We consider on possible applications of the full characteristic decomposition in multi-messenger astronomy, high resolution shock capturing techniques and high energy astrophysical systems such as jet launching, and the modelling accretion disks around black holes. We discuss future work on applying strategies for constraint damping. This is to reduce errors in the numerical approach so that constraint violations are minimized.