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

Abstract

It has recently been demonstrated that Reissner-Nordström 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 positive coupling to the spatially-dependent Maxwell electromagnetic invariant mathcal{F} ≡ FμνFμν 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 ∙ Q ≠ 0 of both the spin a ≡ 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 critical onset line (a/r+)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<frac{Q}{M}le sqrt{2sqrt{2}-2} if their dimensionless spin parameters lie above the critical onset line frac{a(Q)}{M}ge {left[frac{a(Q)}{M}right]}_{mathrm{critical}}=frac{1+sqrt{1-2left(2-sqrt{2}right){left(Q/Mright)}^2}}{2sqrt{2}} .