Paczyński–Wiita potential

${\displaystyle \Phi _{PW}(r)=-{\frac {GM}{r-r_{g}}}}$
where ${\displaystyle r}$ is the radial distance from the black hole, ${\displaystyle G}$ is the gravitational constant, ${\displaystyle M}$ is the mass of the black hole, and ${\displaystyle r_{g}=2GM/c^{2}}$ is its Schwarzschild radius. (${\displaystyle c}$ is the speed of light.) The potential exactly reproduces the locations of the innermost stable circular orbit and the marginally bound orbit. It also exactly reproduces the form of the angular momentum and accurately approximates the Keplerian angular velocity and epicyclic frequency. Because the Paczyński–Wiita potential reproduces these general relativistic effects and is easy to calculate, it is widely used in numerical simulations of black hole accretion.