Constraint Damping in the Characteristic Problem of Ideal GRMHD

We investigate the characteristic problem of ideal general relativistic magnetohydrodynamics (GRMHD). We build on previous work that uses conservation laws and Maxwell's equations in an arbitrary, dynamic spacetime to find the characteristic equation and wave speeds for modeling GRMHD numerically. Such simulated systems can accumulate errors from multiple sources as they evolve. This can eventually cause the solution to become non-physical. There are a number of approaches to constrain and even dynamically reduce this error. Here, we discuss extending earlier work on the characteristic problem in GRMHD by including constraint damping of the ∇ · Β = 0 (no magnetic monopoles) constraint. We also consider an approach by which we renormalize the left and right eigenvectors to handle degenerate cases. Taken together, these approaches to GRMHD systems will have bearing on simulations which incorporate high-resolution shock capturing techniques to model jet launching, accretion disks around black holes, and other high-energy astrophysical phenomenon like neutron star mergers.