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 2.5 post-Newtonian order, with lower computational costs than fully relativistic simulations.

Figure 1

The gravitational mass vs radius (in isotropic coordinates) for static and spherically symmetric stars (described by a perfect fluid obeying a polytropic equation of state with $K=100G^3{M}_{\odot }^2/c^6$ and $\Gamma =2$), for the various models presented in Sec. 7, for Newtonian theory, and for general relativity.

Figure 2

The gauge-invariant ISCO radius $R_{\mathrm{ISCO}}=(M{\Omega }_{\mathrm{ISCO}}{)}^{-2/3}$ of an isolated rotating black hole for the various models presented in Sec. 7, for the pseudo-Newtonian PV potential, and for general relativity.