The Transformation of the Rotational Energy of an Accreting Kerr Black Hole

Accretion of matter onto black holes (BHs) is a prevalent phenomenon in the cosmos, resulting in consequential changes to both the mass and irreducible mass of the BH. These alterations significantly impact the rotational energy reservoir harbored within. This study investigates the relationship between the increase in a BH’s irreducible mass and the augmentation of its total mass due to the infall of matter (test particles) from the innermost stable circular orbit (ISCO) of a Kerr BH. Interestingly, the ratio of total mass growth to irreducible mass growth proves to be a non-monotonic function concerning the dimensionless spin parameter. It initially rises with spin, culminating near an extreme BH (\(\hat {a} \simeq 0.998\)), before declining. At the extreme BH position, the ratio is \(\frac{{dM}}{{d{{M}_{{{\text{irr}}}}}}} = \sqrt 2 \), indicating that accretion along the ISCO leads to the ultimate stabilization of the BH as an extreme one. Conversely, massless particles falling along unstable circular orbits exhibit a continuous increasing ratio of total mass growth to irreducible mass growth with respect to the dimensionless spin parameter.