Emilio TejedaS. Rosswog

An improved pseudo-Newtonian description of particle motion in Schwarzschild spacetime

In this talk, I will present a recently derived generalized Newtonian potential that describes particle motion in Schwarzschild spacetime with higher accuracy than other commonly used pseudo-Newtonian approaches. This potential exactly reproduces several relativistic features such as: the location of the marginally stable, marginally bound and photon circular orbits, the binding energy and angular momentum of circular orbits, and the pericentre precession and spatial projection of general trajectories. Other quantities such as the orbital and epicyclic angular frequencies are reproduced to better than 6 per cent. The equations of motion derived from this potential can be easily implemented within existing Newtonian hydrodynamics codes with hardly any additional computational effort. As an example of this, I will show the implementation of the new approach within an SPH code for studying the tidal disruption of a solar-type star by a supermassive black hole.