A numerical method for general relativistic magnetohydrodynamics

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, & Wilson and uses Evans & Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A one-dimensional version of the code (Minkowski metric) was used to verify code performance in the special relativistic limit. The tests include Alfven wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and nonrelativistic shock tubes. A series of one- and two-dimensional tests were also carried out in the Kerr metric: magnetized Bondi in flow, a magnetized in flow test due to Gammie, and two-dimensional magnetized constant-l tori that are subject to the magnetorotational instability.