Morampudi, Manichandra
One of the long standing problems in accretion disk theory is that concerning black holes that accrete at a rate much lower than the Eddington rate. The plasma that constitutes the disk is in a regime where the Coulomb mean free path is much larger than the disk, and the collision time scales are larger than the inflow time. Thus, the plasma is collisionless and is subject to a wide range of kinetic phenomena that are absent from current general relativistic ideal magnetohydrodynamic models. We exploit the gyro ordering of a collisionless magnetized plasma, and use Israel-Stewart formalism to derive a theory, called Extended General Relativistic Magnetohydrodynamics (EMHD), that accounts for up to second order anisotropic dissipative effects. Using detailed linear analysis, we show that the model is conditionally hyperbolic, causal and stable, and does not suffer from pathologies inherent in first order dissipative theories in general relativity. The dissipation in this theory is driven by spatio-temporal gradients of thermodynamic variables. This cannot be handled by current numerical schemes, which have been designed for ideal fluids. To address this, we formulate an algorithm to handle arbitrary hyperbolic theories, and implement this into a new computer code. The code {\tt grim} will allow for an exploration of the solution space of a broad range of relativistic fluid theories that incorporate sophisticated microphysics. It is designed to run on various computer architectures, and to achieve a significant fraction of machine peak. It exhibits near perfect scaling upto 4096 CPU cores, and 256 GPUs. We use it to integrate the EMHD theory in a Kerr space-time of a supermassive black hole, and show that kinetic effects have an O(1)O(1) effect on the structure of an accretion disk. These effects may have observational consequences for Sgr A*, the supermassive black hole at the center of the Milky Way, whose horizon scale dynamics will be imaged by the upcoming Event Horizon Telescope.