Characteristic Ideal GRMHD with Constraint Damping

We consider the characteristic problem in ideal, general relativistic magnetohydrodynamics. Writing the relevant equations in 3+1 and balance law form, we verify the characteristic equation together with the relevant wave speeds. We provide corrections to a previous calculation of the full eigenvalue problem with complete, normalized left and right eigenvectors. We discuss extensions to include constraint damping of the magnetic monopole constraint and renormalizing the eigenvectors to handle degenerate cases. We speculate on possible applications of the full characteristic decomposition in high-resolution shock-capturing techniques and high-energy astrophysical systems such as jet launching.