| Summary: | 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 F $$ \mathcal{F} $$ ≡ F μν F μν 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 = 2 $$ \sqrt{2} $$ − 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 M ≤ 2 2 − 2 $$ 0<\frac{Q}{M}\le \sqrt{2\sqrt{2}-2} $$ if their dimensionless spin parameters lie above the critical onset line a Q M ≥ a Q M critical = 1 + 1 − 2 2 − 2 Q / M 2 2 2 $$ \frac{a(Q)}{M}\ge {\left[\frac{a(Q)}{M}\right]}_{\mathrm{critical}}=\frac{1+\sqrt{1-2\left(2-\sqrt{2}\right){\left(Q/M\right)}^2}}{2\sqrt{2}} $$ .
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