It is important to keep in mind that elements of gas in an accretion
flow do not behave exactly as test particles close to the ISCO, and in
some cases their dynamics can be influenced strongly by pressure and
magnetic forces. Gas (or radiation) pressure forces, directed inward,
can allow gas to remain in orbit slightly closer to the black hole than
the ISCO, and with somewhat higher angular momentum. Gas plunging into
the black hole from such an orbit would have a lower binding energy and
therefore a lower accretion efficiency. In the limiting case where gas
orbits a Schwarzschild black hole down to 4*M* (the *marginally
bound orbit*), the binding energy of the accreted gas approaches zero
and so does the accretion efficiency
[2].

Likewise, net magnetic flux, accumulating in the innermost regions of an
accretion flow, could hold back the gas, creating a *magnetically
arrested disk*
[3].
The angular momentum close to the black hole might then be lower than
that of any stable test particle orbit, but infall could be regulated by
interactions between the gas and the magnetic field, such as interchange
instabilities and reconnection.

In light of these considerations, we can identify at least four factors that must play an important role in governing black hole accretion flows. The first three of these may be regarded as outer boundary conditions for the problem.

. The specific angular momentum at the marginally bound orbit, somewhat larger than ℓ__Angular momentum___{ISCO}but still of order a few*GM*/*c*, represents the largest angular momentum per unit mass that can be accreted by a black hole. Given that the radius of the gas reservoir supplying black hole accretion is usually at least a few hundred times*M*, and often much more, accretion is seldom possible without the loss of some angular momentum. Angular momentum is thought to be transferred outward through the flow via the magnetorotational instability (MRI) [4], which works in the limit of sufficiently*weak*magnetic field. Angular momentum can also be lost through winds or electromagnetic torques; the latter process depends on net magnetic flux, the third factor below.. Energy liberated during the accretion process is thought to be transferred outward by the same processes that wick away the excess angular momentum. Some of this energy can go into driving coherent motions such as circulations or outflows, or can be removed by electromagnetic torques. [5]. But much (or most) of it is likely to be dissipated as heat or radiation. If much of this energy is retained by the flow, the associated pressure can partially support the flow against gravity, reducing the relative importance of rotation. When the local rotation rate is still a large fraction of the Keplerian value, the flow resembles a disk but the added pressure force can drive circulation or even mass loss [6, 7]. When pressure support dominates rotational support, or even becomes comparable to it, the flow can inflate into a nearly spherical configuration and interesting stability questions arise.__Radiative efficiency__. The MRI basically uses distortions of a poloidal magnetic field (i.e., parallel to the rotation axis) to extract free energy from differential rotation [4]. Therefore, it is not surprising that the vigor of angular momentum transport driven by MRI is sensitive to the presence of poloidal magnetic flux [8]. Recent numerical experiments [9] suggest that a poloidal magnetic pressure as small as 0.1% of the gas pressure, coherent over scales comparable to the disk thickness, is enough to enhance angular momentum transport by a substantial factor. Small patches of magnetic flux could arise through statistical fluctuations as a result of local MRI [10] but larger coherent fields probably need to be accumulated by advection of flux from larger distances. Whether efficient flux advection is possible is highly uncertain [11], and probably depends sensitively on details of the distant outer boundary conditions [12] and vertical disk structure [13]. Sufficiently coherent poloidal magnetic flux, threading the innermost regions of the rotating accretion flow, is an essential element for extracting rotational energy from the black hole, and presumably also for producing a strong disk wind.__Magnetic flux__. Part of the gravitating mass__Black hole spin__*M*of a spinning black hole, as perceived by a distant observer, is contributed by the spin energy. In principle, all of this energy — up to 0.29*M*for an extreme Kerr hole — can be extracted. In practice this can be done using coherent poloidal magnetic fields, through the Blandford–Znajek (BZ) process [14]. Since the power extracted is proportional to the square of the net magnetic flux threading the hole as well as the square of the spin parameter*a*, the efficiency of the BZ effect is sensitive to the amount of flux that can be accumulated and held in place against the black hole. Analytic calculations and relativistic magnetohydrodynamic simulations show that the efficiency can be appreciable, possibly even exceeding the efficiency of the accretion process [15, 16].