Horizon Instability of Extremal Kerr Black Holes: Nonaxisymmetric Modes and Enhanced Growth Rate

TL;DR

This paper investigates the horizon instability of extremal Kerr black holes, revealing a connection to singularities in the Green function and demonstrating enhanced growth rates for nonaxisymmetric modes influenced by conformal weights.

Contribution

It identifies the role of a singular branch point in the Green function in horizon instability and analyzes the impact of nonaxisymmetric modes on growth rates.

Findings

Horizon instability linked to a singular branch point at superradiant frequency.

Enhanced growth rates for nonaxisymmetric modes depending on conformal weights.

Potential implications for near-extremal black holes and holographic duality.

Abstract

We show that the horizon instability of the extremal Kerr black hole is associated with a singular branch point in the Green function at the superradiant bound frequency. We study generic initial data supported away from the horizon and find an enhanced growth rate due to nonaxisymmetric modes. The growth is controlled by the conformal weight of each mode. We speculate on connections to near-extremal black holes and holographic duality.