Black-hole (BH) accretion and mergers drive BH growth and power the most energetic phenomena in the universe, yet how much energy is retained as transformable rotational energy remains unclear. Using the irreducible mass to split a Kerr BH into an irreversible part and a transformable rotational reservoir, we trace the evolution of each energy channel and compare the radiated and stored energies across different BH growth processes. For prograde conservative accretion through the innermost stable circular orbit, the rotational energy gained exceeds the radiated energy over the broad spin range (0.0722<a<0.9993), the result preserved by radiation-reaction corrections up to just below the corresponding saturation spins. Numerical-relativity merger fits show that, for quasicircular nonspinning binaries, stored rotational energy in the remnant exceeds radiated energy for mass ratios (q>0.0894); this relation also holds across most of the eccentricities and spin configurations explored. Observationally, all LIGO–Virgo–KAGRA events from O1-O4 with publicly reported source parameters satisfy this relation. Our studies connect BH thermodynamics, growth, and energy extraction, showing that across most astrophysically relevant parameters, BH growth builds a rotational reservoir larger than the energy it directly radiates. This result helps us understand energy supply and transfer in extreme environments and enables studies of energy extraction from BHs to be more astrophysically meaningful.
Shurui Zhang is currently a postdoctoral fellow at ICRANet. He received PhD degrees from both the University of Ferrara and USTC (University of Science and Technology of China). His research interests are on AGNs and compact objects via multi-messenger approaches.
ICRANet