General Overview of Black Hole Accretion Theory

I provide a broad overview of the basic theoretical paradigms of black hole accretion flows. Models that make contact with observations continue to be mostly based on the four decade old alpha stress prescription of Shakura & Sunyaev (1973), and I discuss the properties of both radiatively efficient and inefficient models, including their local properties, their expected stability to secular perturbations, and how they might be tied together in global flow geometries. The alpha stress is a prescription for turbulence, for which the only existing plausible candidate is that which develops from the magnetorotational instability (MRI). I therefore also review what is currently known about the local properties of such turbulence, and the physical issues that have been elucidated and that remain uncertain that are relevant for the various alpha-based black hole accretion flow models.