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 timedependent hydrodynamic simulations to study the temporal behavior of such accretion disks.