Magnetic fields play a central role in black hole astrophysics, powering relativistic jets and other energetic phenomena. While near-horizon magnetic field is usually assumed to originate from the accretion flow, additional large-scale magnetic fields—such as those supplied by a companion neutron star in stellar-mass binaries or by galactic fields around supermassive black holes—may also affect the horizon-threading flux. In this work, we study the superposition of a weak arbitrarily inclined external uniform magnetic field with the internal Blandford–Znajek split-monopole field around a Schwarzschild black hole. This setup generically gives rise to magnetic null points, where the total field vanishes. We compute the magnetic flux through an arbitrarily tilted hemisphere of the event horizon and show that the flux can be substantially suppressed by the external field. In the axisymmetric case, the flux can even vanish completely. However, with nonzero inclination, complete cancellation becomes impossible, despite significant reduction. We further explore the ionization and subsequent particle acceleration from a Keplerian accretion disk, finding that efficient collimated outflows persist even under significant field inclination. We show that the acceleration is critically dependent on the external field orientation, with the escape fraction maximized at nonzero inclinations due to the destabilization of trapping zones and vanishing in the antialigned configuration, where closed magnetic loops effectively suppress the outflow. We discuss the astrophysical implications of these findings, proposing that geometric flux cancellation can serve as a mechanism for jet quenching in compact binaries and offering an explanation for the lack of a prominent large-scale jet in Sgr A*.

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• Classical black holes
• Magnetic field generation & plasma dynamo
• Accretion disk & black-hole plasma