Scalar perturbations on the background of Kerr black holes in the quadratic dynamical Chern-Simons gravity

TL;DR

This paper investigates scalar perturbations around Kerr black holes in quadratic dynamical Chern-Simons gravity, revealing potential instabilities that could lead to black hole scalarization, using numerical time-domain analysis.

Contribution

It provides the first numerical analysis of scalar perturbations on Kerr black holes in this modified gravity, identifying conditions for instability and possible scalarization.

Findings

Kerr black holes can become unstable under scalar perturbations in this theory.

The instability depends on the azimuthal mode number m.

Potential for spontaneous scalarization into non-Kerr black holes.

Abstract

We study the scalar perturbation on the background of a Kerr black hole in the dynamical Chern-Simons modified gravity with a quadratic coupling between the scalar field and Chern-Simons term. In particular, the late-time tails of scalar perturbations are investigated numerically in time domain by using the hyperboloidal foliation method. It is found that the Kerr black hole becomes unstable under linear perturbations in a certain region of the parameter space, which depends on the harmonic azimuthal index $m$ of the perturbation's mode. This may indicate that some Kerr black holes in this theory will get spontaneously scalarized into a non-Kerr black hole.