Onset of rotating scalarized black holes in Einstein-Chern-Simons-Scalar theory

TL;DR

This paper investigates the stability of Kerr black holes in Einstein-Chern-Simons-Scalar theory, revealing instabilities for positive and negative coupling parameters through analytical and numerical methods.

Contribution

It introduces a hyperboloidal foliation method to analyze black hole stability in this modified gravity theory, demonstrating new instability regimes.

Findings

Kerr black holes are unstable for positive coupling parameter.

Unbounded instability occurs for negative coupling parameter.

The hyperboloidal foliation method effectively analyzes black hole perturbations.

Abstract

We perform the stability analysis of the Kerr black hole in the Einstein-Chern-Simons-Scalar theory with quadratic scalar coupling. For positive coupling parameter ($\alpha>0$), we introduce the (2+1)-dimensional hyperboloidal foliation method to show that the Kerr black hole is unstable against scalar-mode perturbation. In case of $\alpha<0$, it is shown that the Kerr black hole is unstable without any $\alpha$-independent bound on the rotation parameter $a$ when using the the hyperboloidal foliation method. The disappearance of the $a$-bound is confirmed analytically by implementing the (1+1)-dimensional linearized scalar equation.