Dyonic hairy black holes in $U(1)$ gauge-invariant scalar-vector-tensor theories: Cubic and quartic interactions

TL;DR

This paper constructs and classifies new asymptotically flat black hole solutions with scalar and vector hair in gauge-invariant theories, highlighting the role of magnetic charge and higher-order interactions in their properties.

Contribution

It extends previous models by systematically including cubic and quartic interactions in scalar-vector-tensor theories with magnetic charge, revealing new solution branches and interaction effects.

Findings

Magnetic charge activates specific interaction sectors like cubic coupling.

Solutions exhibit primary or secondary hair depending on symmetry properties.

Scalar hair decay rates vary with interaction types, affecting observational signatures.

Abstract

We construct and classify asymptotically flat, static, spherically symmetric hairy black hole solutions in $U(1)$ gauge-invariant scalar-vector-tensor (SVT) theories carrying both electric and magnetic charges. Extending previous studies beyond the quadratic sector, we systematically incorporate cubic and quartic interaction terms in the presence of the magnetic charge. We derive a consistency condition for the quartic interaction that eliminates higher-order derivative terms induced by the magnetic charge, ensuring the theory remains second-order. We classify the obtained solutions based on their symmetry properties: shift-symmetric couplings yield secondary hair governed by the Noether current, whereas $\phi$-dependent interactions generate primary hair. Crucially, our analysis reveals that the magnetic charge plays a key role in activating specific interaction sectors such as the cubic coupling $\tilde{f}_3$, which does not appear in the field equations in purely electric configurations. We identify solution branches that are intrinsic to the magnetic charge, as they cease to exist in the vanishing monopole limit ($P\to 0$). Furthermore, we demonstrate that the scalar hair exhibits distinct asymptotic decay rates depending on the interaction type, suggesting possible variations in observational signatures. Finally, we verify the global regularity of these solutions by connecting analytic expansions with numerical integration.