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 ${ { a(Q)}\over{ M}}\geq \big[{ { a(Q)}\over{ M}}\big]_{ \text{ critical}}={ { 1+\sqrt{ 1-2(2-\sqrt{ 2}){ (Q/M)}^2}}\over{ 2\sqrt{ 2}}}$.
Categories: gr-qc astro-ph.HE hep-th