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We compute the radiation emitted by a particle on the innermost stablecircular orbit of a rapidly spinning black hole both (a) analytically, workingto leading order in the deviation from extremality and (b) numerically, with anew high-precision Teukolsky code. We find excellent agreement between the twomethods. We confirm previous estimates of the overall scaling of the powerradiated, but show that there are also small oscillations all the way toextremality. Furthermore, we reveal an intricate mode-by-mode structure in theflux to infinity, with only certain modes having the dominant scaling. Thescaling of each mode is controlled by its conformal weight, a quantity thatarises naturally in the representation theory of the enhanced near-horizonsymmetry group. We find relationships to previous work on particles orbiting inprecisely extreme Kerr, including detailed agreement of quantities computedhere with conformal field theory calculations performed in the context of theKerr/CFT correspondence.

Particle on the Innermost Stable Circular Orbit of a Rapidly Spinning Black Hole