Pseudo-Newtonian potentials to describe the temporal effects on relativistic accretion disks around rotating black holes and neutron stars

Two pseudo-Newtonian potentials, which approximate the angular and epicyclic frequencies of the relativistic accretion disk around rotating (and counter-rotating) compact objects, are presented. One of them, the logarithmically modified potential, is a better approximation for the frequencies while the other, the second-order expanded potential, also reproduces the specific energy for circular orbits in close agreement with the general relativistic values. These potentials may be included in time-dependent hydrodynamic simulations to study the temporal behavior of such accretion disks.