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

TL;DR

This paper analyzes radiation from a particle orbiting near the innermost stable circular orbit of a rapidly spinning black hole, combining analytical and numerical methods to reveal detailed mode structures and scaling behaviors.

Contribution

It introduces a high-precision Teukolsky code and provides new insights into mode-specific flux scaling and oscillations near extremality, connecting to Kerr/CFT correspondence.

Findings

Excellent agreement between analytical and numerical results.

Identification of mode-specific scaling governed by conformal weights.

Discovery of small oscillations in radiated power approaching extremality.

Abstract

We compute the radiation emitted by a particle on the innermost stable circular orbit of a rapidly spinning black hole both (a) analytically, working to leading order in the deviation from extremality and (b) numerically, with a new high-precision Teukolsky code. We find excellent agreement between the two methods. We confirm previous estimates of the overall scaling of the power radiated, but show that there are also small oscillations all the way to extremality. Furthermore, we reveal an intricate mode-by-mode structure in the flux to infinity, with only certain modes having the dominant scaling. The scaling of each mode is controlled by its conformal weight, a quantity that arises naturally in the representation theory of the enhanced near-horizon symmetry group. We find relationships to previous work on particles orbiting in precisely extreme Kerr, including detailed agreement of quantities computed here with conformal field theory calculations performed in the context of the Kerr/CFT correspondence.