Whirling orbits around twirling black holes from conformal symmetry

TL;DR

This paper explores how near-horizon conformal symmetry in rapidly rotating Kerr black holes relates unstable orbits to physical trajectories, enabling analytical computation of radiation and self-force effects.

Contribution

It introduces a novel use of conformal symmetry to connect unstable orbits with physical plunges and derives analytical formulas for radiation and self-force on these trajectories.

Findings

Unstable orbits are related to physical plunges via conformal transformations.

Analytical expressions for radiation emitted by these orbits are provided.

A simple formula for the self-force on such trajectories is derived.

Abstract

Dynamics in the throat of rapidly rotating Kerr black holes is governed by an emergent near-horizon conformal symmetry. The throat contains unstable circular orbits at radii extending from the ISCO down to the light ring. We show that they are related by conformal transformations to physical plunges and osculating trajectories. These orbits have angular momentum arbitrarily higher than that of ISCO. Using the conformal symmetry we compute analytically the radiation produced by the physical orbits. We also present a simple formula for the full self-force on such trajectories in terms of the self-force on circular orbits.