= Solution
The <maximal radiative efficiency of black-hole accretion> is the fraction of rest-mass energy available if all binding energy released before capture escapes as radiation. In a Newtonian disk ending at $R_{\rm in}$,
$$
\eta_{\max}=\frac{GM}{2R_{\rm in}c^2},
$$
because a circular orbit has specific binding energy $GM/(2R)$. In relativity, $\eta_{\max}=1-E_{\rm ISCO}$. Black-hole spin moves the <innermost stable circular orbit> inward for prograde flow and outward for retrograde flow, increasing or decreasing this maximum respectively.
Since $L=\eta\dot M c^2$, a source of fixed luminosity requires $\dot M=L/(\eta c^2)$, while black-hole mass grows at approximately $(1-\eta)\dot M$. The actual <radiative efficiency of black-hole accretion> can lie below the maximum when energy is advected through the horizon or carried away mechanically. A low-density, optically thin <advection-dominated accretion flow> stores dissipated energy in ions, while a high-rate <slim accretion disk> traps photons and advects their energy inward; both are <radiatively inefficient accretion flow>[radiatively inefficient flows].
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