Scalar Self-force for High Spin Black Holes

TL;DR

This paper analytically studies the scalar self-force on particles near nearly extremal Kerr black holes, revealing universal behaviors and linking local forces with radiation fluxes through conformal symmetry insights.

Contribution

It introduces a semi-analytical method leveraging near-horizon conformal symmetry to compute the scalar self-force for generic geodesics in high-spin black holes.

Findings

Angular component of self-force is universal at leading order.

Energy and angular momentum losses match scalar radiation fluxes.

Persistent oscillations relate to traveling waves affecting force and flux decoupling.

Abstract

We semianalytically investigate the scalar self-force experienced in the final stages of extreme mass ratio inspirals of nonspinning scalar particles into supermassive nearly extremal Kerr black holes. We exploit the near-horizon conformal symmetry to find the self-force for general corotating equatorial geodesics. The angular component of the self-force is shown to be universal at leading order in the high spin limit. We verify that the energy and angular momentum losses of the scalar particle match with the asymptotic fluxes of scalar radiation. In particular, we relate the previously described persistent oscillations in the asymptotic energy and angular momentum fluxes with the local self-force. Such oscillations arise from traveling waves that prevent the near-horizon and the asymptotic region to fully decouple in the extremal limit. Conformal invariance is therefore reduced to discrete scale invariance with associated logarithmic periodicity.