We extend our previous Schwarzschild metric-based studies of gravitational-electromagnetic (GEM) coupling to rotating black holes by working directly in a curvature-based Newman-Penrose/Teukolsky framework on Kerr spacetime. Within a minimally coupled Einstein-Maxwell system, we derive explicit quadratic electromagnetic source terms for the spin-$-2$ Teukolsky equation, providing a foundation for future numerical studies of GEM interactions in the framework of black-hole spectroscopy. Moreover, we give order-of-magnitude arguments showing that GEM quadratic quasinormal modes (QQNMs) can become relevant in a range of charged and magnetized astrophysical scenarios. Finally, we show through a brief dilaton-theory example that the GEM QQNM spectrum is sensitive to how gravity couples to electromagnetism, thereby providing a model-based way to test minimal coupling and to constrain hidden $U(1)$ sectors with gravitational-wave observations.

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• Alternative gravity theories
• Classical black holes
• Dark matter
• General relativity
• Gravitational waves
• Binary stars
• Neutron stars & pulsars