  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.
