Tidal disruptions by rotating black holes: relativistic hydrodynamics with Newtonian codes

We propose an approximate approach for studying the relativistic regime of stellar tidal disruptions by rotating massive black holes. It combines an exact relativistic description of the hydrodynamical evolution of a test fluid in a fixed curved spacetime with a Newtonian treatment of the fluid's self-gravity. Explicit expressions for the equations of motion are derived for Kerr spacetime using two different coordinate systems. We implement the new methodology within an existing Newtonian Smoothed Particle Hydrodynamics code and show that including the additional physics involves very little extra computational cost. We carefully explore the validity of the novel approach by first testing its ability to recover geodesic motion, and then by comparing the outcome of tidal disruption simulations against previous relativistic studies. We further compare simulations in Boyer--Lindquist and Kerr--Schild coordinates and conclude that our approach allows accurate simulation even of tidal disruption events where the star penetrates deeply inside the tidal radius of a rotating black hole. Finally, we use the new method to study the effect of the black hole spin on the morphology and fallback rate of the debris streams resulting from tidal disruptions, finding that while the spin has little effect on the fallback rate, it does imprint heavily on the stream morphology, and can even be a determining factor in the survival or disruption of the star itself. Our methodology is discussed in detail as a reference for future astrophysical applications.