Revisited equilibrium solution of Fishbone and Moncrief torus for extended GRMHD simulations

Accretion physics has become more important recently due to the detection of the first horizon-scale images of the super-massive black holes of M\,87$^*$ and Sgr~A$^*$ by the Event Horizon Telescope (EHT). General relativistic magnetohydrodynamic (GRMHD) simulations of magnetized accretion flows onto a Kerr black hole have been used to interpret them. However, further testing the theory of gravity by using horizon-scale images requires performing consistent GRMHD simulations in non-Kerr spacetime. In this paper, we revisited the hydrodynamical equilibrium solution of the Fishbone and Moncrief (FM) torus that can be used to study any stationary, axisymmetric, vacuum, or non-vacuum spacetime. Further, we check the stability of the FM torus in non-Kerr spacetime by general relativistic hydrodynamic simulations. We find that FM torus in non-Kerr spacetime is indeed stable under long-term evolution. We conclude that the generalized FM torus solution would be very useful for creating new GRMHD libraries in extended Kerr black holes.