On incorporating post-Newtonian effects in N-body dynamics

Understand

The increasing role of general relativity in the dynamics of stellar systems with central massive black holes and in the evolution of hierarchical triple systems inspires a close examination of how post-Newtonian effects are incorporated into N-body dynamics.

• The majority of approaches incorporate relativity by adding to the Newtonian N-body equations the standard two-body post-Newtonian terms for a given star around the black hole or for the close binary in a triple system.
• We argue that, for calculating the evolution of such systems over timescales comparable to the relativistic pericenter advance timescale, it is essential to include "cross terms" in the equations of motion.
• These are post-Newtonian terms that represent a coupling between the potential of the central black hole and the potential due to other stars in the system.