Instabilities in Kerr Spacetimes

TL;DR

This paper investigates the stability of Kerr spacetimes under various gravitational and field perturbations, revealing an infinite family of unstable modes that challenge previous assumptions about their stability.

Contribution

It generalizes prior stability analyses by including multiple field types and demonstrates the existence of infinite unstable modes in Kerr spacetimes.

Findings

Existence of infinite unstable modes in Kerr spacetimes.

Unstable modes found for electromagnetic, Dirac, and scalar field perturbations.

Extended stability analysis beyond the Cauchy horizon.

Abstract

We present a generalization of previous results regarding the stability under gravitational perturbations of nakedly singular super extreme Kerr spacetime and Kerr black hole interior beyond the Cauchy horizon. To do so we study solutions to the radial and angular Teukolsky's equations with different spin weights, particulary $s=\pm 1$ representing electromagnetic perturbations, $s=\pm 1/2$ representing a perturbation by a Dirac field and $s=0$ representing perturbations by a scalar field. By analizing the properties of radial and angular eigenvalues we prove the existence of an infinite family of unstable modes.