Stability study of a model for the Klein-Gordon equation in Kerr space-time II

TL;DR

This paper provides rigorous mathematical proof for the instability of scalar fields around rotating black holes, refining previous numerical results and extending the understanding of the Klein-Gordon equation in Kerr space-time.

Contribution

It offers the first rigorous proof of the instability threshold for scalar fields in Kerr space-time, improving upon earlier numerical estimates.

Findings

Rigorous proof of instability down to a/M ≈ 0.9798

Refinement of previous numerical instability threshold

Supports the physical understanding of scalar field behavior in Kerr black holes

Abstract

The present paper is a follow-up of our previous paper that derives a slightly simplified model equation for the Klein-Gordon equation, describing the propagation of a scalar field of mass $\mu$ in the background of a rotating black hole and, among others, supports the instability of the field down to $a/M \approx 0.97$. The latter result was derived numerically. This paper gives corresponding rigorous results, supporting instability of the field down to $a/M \approx 0.979796$.