Spin-Charge induced spontaneous scalarization of Kerr-Newman black holes

TL;DR

This paper explores the conditions under which Kerr-Newman black holes spontaneously develop scalar fields due to tachyonic instability in Einstein-Maxwell-scalar theory, revealing that high rotation promotes scalarization without a lower bound on rotation.

Contribution

It provides a numerical analysis of the onset surface for spontaneous scalarization of Kerr-Newman black holes in EMS theory, highlighting the role of rotation and charge.

Findings

High rotation enhances scalarization.

No lower bound on rotational parameter for scalarization.

Upper bound on rotation given by charge and mass relation.

Abstract

We investigate the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell-scalar (EMS) theory with a positive coupling parameter $\alpha$. This corresponds to exploring the onset of spontaneous scalarization for KN black holes. For this purpose, we use the hyperboloidal foliation method (HFM) to solve the linearized scalar equation numerically. We obtain a 3D graph [$\log_{10}\alpha(a,Q)$] which indicates the onset surface for spontaneous scalarization of KN black holes in the EMS theory. We find that there is no lower bound on the rotational parameter $a$, but its upper bound is given by $M^2-Q^2 \ge a^2$. Also, we confirm that the high rotation enhances spontaneous scalarization of KN black holes in the EMS theory.