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We adopt the fluid conduction approximation to study the evolution ofspherical star clusters and self-interacting dark matter (SIDM) halos. We alsoexplore the formation and dynamical impact of density cusps that arise in bothsystems due to the presence of a massive, central black hole. The large N-body,self-gravitating systems we treat are "weakly-collisional": the mean free timebetween star or SIDM particle collisions is much longer than theircharacteristic crossing (dynamical) time scale, but shorter than the systemlifetime. The fluid conduction model reliably tracks the "gravothermalcatastrophe" in star clusters and SIDM halos without black holes. For a starcluster with a massive, central black hole, this approximation reproduces thefamiliar Bahcall-Wolf quasistatic density cusp for the stars bound to the blackhole and shows how the cusp halts the "gravothermal catastrophe" and causes thecluster to re-expand. An SIDM halo with an initial black hole central densityspike that matches onto to an exterior NFW profile relaxes to a core-halostructure with a central density cusp determined by the velocity dependence ofthe SIDM interaction cross section. The success and relative simplicity of thefluid conduction approach in evolving such "weakly-collisional",quasiequilibrium Newtonian systems motivates its extension to relativisticsystems. We present a general relativistic extension here.

Star Clusters, Self-Interacting Dark Matter Halos and Black Hole Cusps: The Fluid Conduction Model and its Extension to General Relativity