It is widely accepted that magnetic reconnections occur successively in black hole accretion flows, especially on the equatorial plane, owing to the formation of the equatorial current sheet. When magnetic reconnection takes place within the ergosphere of a rotating black hole, one of the ejected plasmoids (denoted as ${\mathrm{p}}^{-}$) may acquire negative energy-at-infinity density, while the companion plasmoid (denoted as ${\mathrm{p}}^{+}$) correspondingly carries the energy extracted from the black hole. This mechanism, known as the Comisso-Asenjo process, provides a viable astrophysical pathway for extracting energy from a rotating black hole. Generally speaking, two conditions have to be satisfied for successful energy extraction. First, ${\mathrm{p}}^{-}$ is generated via magnetic reconnection with negative energy-at-infinity density. Second, the associated ${\mathrm{p}}^{+}$, which carries the extracted energy, must escape to infinity. Though a number of studies have promoted the theory of the Comisso-Asenjo process, the escape of ${\mathrm{p}}^{+}$ lacks consideration. In this work, we adopt geodesic approach to systematically examine the destinies of ${\mathrm{p}}^{+}$ after ejection, thereby establishing the complete conditions for energy extraction from a rotating black hole via magnetic reconnection. We redefine the covering factor, for which only escaping ${\mathrm{p}}^{+}$ are counted. This quantity reflects how probable the successful energy extraction occurs in an accretion system. Through analysis of this revised covering factor, we identify a lower bound on the black hole spin, $a=0.8005$, below which energy extraction via magnetic reconnection can never succeed, no matter how high the magnetization of the bulk plasma is. This limit suggests that the spin-down of a black hole caused by successive magnetic reconnections would terminate once the spin decreases to approximately 0.8005.

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• Astrophysical fluid dynamics
• Classical black holes
• Magnetic reconnection
• Magnetohydrodynamics
• Accretion disk & black-hole plasma