A Post-Newtonian approach to black hole-fluid systems

This work devises a formalism to obtain the equations of motion for a black hole-fluid configuration. Our approach is based on a Post-Newtonian expansion and adapted to scenarios where obtaining the relevant dynamics requires long time-scale evolutions. These systems are typically studied with Newtonian approaches, which have the advantage that larger time-steps can be employed than in full general-relativistic simulations, but have the downside that important physical effects are not accounted for. The formalism presented here provides a relatively straightforward way to incorporate those effects in existing implementations, up to 2.5PN order, with lower computational costs than fully relativistic simulations.