Modified Newtonian Potentials for the Description of Relativistic Effects in Accretion Disks around Black Holes

We present modified Newtonian potentials to describe the general relativistic effects that are most important for accretion disk structure around nonrotating and rotating black holes. We compare disk solutions obtained using these potentials with solutions using other potentials that have been proposed in the literature, as well as with the general relativistic solutions. We demonstrate that simple potentials can capture the essentials of general relativity and reproduce the accretion disk structure to an accuracy of about 10%-20%, even for maximally rotating black holes.