Slowly rotating black holes and their scalarization

TL;DR

This paper investigates the conditions under which slowly rotating black holes in Einstein-scalar-Gauss-Bonnet-Chern-Simons theory become unstable and undergo scalarization, revealing instability for positive coupling but not for negative.

Contribution

It introduces a method to analyze tachyonic instability in slowly rotating black holes and identifies the stability boundary using hyperboloidal foliation.

Findings

Unstable against scalar modes for positive coupling .

No tachyonic instability found for negative coupling .

Threshold curves delineate stability and instability regions.

Abstract

We study scalarization of slowly rotating black holes in the Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In the slow rotation approximation of $a\ll1$ with rotation parameter $a$, the GB term is given by a term for Schwarzschild black hole, whereas the CS term takes a linear term of $a$. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. We use the (2+1)-dimensional hyperboloidal foliation method to show the tachyonic instability for slowly rotating black holes by considering the time evolution of a spherically symmetric scalar mode. A threshold (existence) curve is obtained from the constant scalar modes under time evolution, which means the boundary between stable and unstable black holes. It is found that the slowly rotating black holes turn out to be unstable against a spherically symmetric scalar-mode propagation for positive coupling $\alpha$. However, we could not find tachyonic instability and any $a$-bound for scalarization for negative coupling $\alpha$.