Spin-charge induced scalarization of Kerr-Newman black-hole spacetimes

TL;DR

This paper demonstrates that Kerr-Newman black holes can support scalar fields with positive coupling to electromagnetic invariants, leading to a spontaneous scalarization phenomenon dependent on their spin and charge, with a specific critical onset condition.

Contribution

It reveals the novel possibility of positive-coupling scalarization in Kerr-Newman black holes and analytically determines the critical conditions for its onset.

Findings

Scalar fields with positive coupling can be supported in Kerr-Newman spacetimes.

The scalarization occurs when the black hole's spin and charge satisfy a specific critical relation.

The critical onset line for scalarization is explicitly derived for Kerr-Newman black holes.

Abstract

It has recently been demonstrated that Reissner-Nordstr\"om black holes in composed Einstein-Maxwell-scalar field theories can support static scalar field configurations with a non-minimal negative coupling to the Maxwell electromagnetic invariant of the charged spacetime. We here reveal the physically interesting fact that scalar field configurations with a non-minimal {\it positive} coupling to the spatially-dependent Maxwell electromagnetic invariant ${\cal F}\equiv F_{\mu\nu}F^{\mu\nu}$ can also be supported in black-hole spacetimes. Intriguingly, it is explicitly proved that the positive-coupling black-hole spontaneous scalarization phenomenon is induced by a non-zero combination $a\cdot Q\neq0$ of {\it both} the spin $a\equiv J/M$ and the electric charge $Q$ of the central supporting black hole. Using analytical techniques we prove that the regime of existence of the positive-coupling spontaneous scalarization phenomenon of Kerr-Newman black holes with horizon radius $r_+(M,a,Q)$ and a non-zero electric charge $Q$ (which, in principle, may be arbitrarily small) is determined by the {\it critical onset line} $(a/r_+)_{\text{critical}}=\sqrt{2}-1$. In particular, spinning and charged Kerr-Newman black holes in the composed Einstein-Maxwell-scalar field theory are spontaneously scalarized by the positively coupled fields in the dimensionless charge regime $0<{{Q}\over{M}}\leq\sqrt{2\sqrt{2}-2}$ if their dimensionless spin parameters lie above the critical onset line ${{a(Q)}\over{M}}\geq \big[{{a(Q)}\over{M}}\big]_{\text{critical}}={{1+\sqrt{1-2(2-\sqrt{2}){(Q/M)}^2}}\over{2\sqrt{2}}}$.