An accurate Newtonian description of particle motion around a Schwarzschild black hole

Understand

A generalized Newtonian potential is derived from the geodesic motion of test particles in Schwarzschild spacetime.

• This potential reproduces several relativistic features with higher accuracy than commonly used pseudo-Newtonian approaches.
• The new potential reproduces the exact location of the marginally stable, marginally bound, and photon circular orbits, as well as the exact radial dependence of the binding energy and the angular momentum of these orbits.
• Moreover, it reproduces the orbital and epicyclic angular frequencies to better than 6%.