Impact of Schwarzschild black hole's gravity upon the Rossby wave   instability
  In an early work the Rossby Wave Instability (RWI) has been proposed to explain variability thought to originate in the close vicinity of black-holes but this was done in the pseudo-Newtonian approach. Here we present the first general relativistic hydrodynamics simulations of this instability not only proving its theorized existence in a full general relativistic (GR) environment but also studying the effect of the strong gravity on the instability. To that end we performed a set of simulations increasingly closer to the black hole with our new GR version of the MPI-AMRVAC code.This allows us to study the minute changes in the behaviour of the instability.We found that the pseudo-Newtonian approach gives adequate results provided that time shifting induced by the black hole gravity is taken into account. Hence, to view the disc as a distant observer would a full GR ray-tracing post treatment of the simulations is a must. 
F. Casse, P. Varniere and Z. Meliani
astro-ph.HE