Scalarization of slowly rotating black holes

TL;DR

This paper studies how slowly rotating black holes can develop scalar fields in Einstein-scalar-Chern-Simons theory, revealing conditions under which they become unstable and spontaneously scalarize.

Contribution

It demonstrates the instability of slowly rotating black holes against scalar perturbations in EsCS theory, highlighting the role of the coupling constant and rotation parameter.

Findings

Positive coupling $\alpha$ leads to instability in slowly rotating black holes.

Negative coupling causes instability regardless of rotation speed.

Instability is linked to tachyonic modes indicating scalarization onset.

Abstract

It is interesting to note that most black holes are born very slowly rotating. We investigate scalarization of slowly rotating black holes in the Einstein-scalar-Chern-Simons (EsCS) theory. In the slow rotation approximation, the CS term takes a linear form of rotation parameter $a$ which determines the tachyonic instability. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. It is shown that the slowly rotating black holes are unstable against a spherically symmetric scalar-mode perturbation for positive coupling $\alpha$, whereas these black holes are unstable for negative coupling without any $a$-bound.