Title: Tidal disruptions by rotating black holes: relativistic hydrodynamics with Newtonian codes,
Abstract: 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.