We perform fully relativistic general-relativistic magnetohydrodynamics simulations of magnetized, self-gravitating black hole disk (BHD) systems in which the black hole spin is misaligned with the disk angular momentum. Massive disks (disk to black hole mass ratios of 16%–28%) around rapidly rotating black holes ($\chi \lesssim 0.97$) develop a nonaxisymmetric instability for tilt angles from 0° to 180°. Magnetic stresses damp, but do not completely suppress, the nonaxisymmetric instability, and corresponding gravitational wave emission, in aligned systems, while they enhance it in antialigned BHDs: magnetorotational instability (MRI) driven turbulence enhances angular momentum transport and accelerates nonlinear instability evolution in misaligned configurations. All models launch magnetically driven jets consistent with the Blandford-Znajek mechanism, with collimation depending on spin orientation. The gravitational waves reflect strong nonaxisymmetric structure from a persistent $m=1$ mode. The coupling between fast MRI and the slower nonaxisymmetric instability growth governs the outcome, with tilt controlling how MRI modifies the global mode. These simulations provide the first self-consistent general-relativistic magnetohydrodynamics treatment of tilted, self-gravitating BHD systems and support their role as multimessenger sources.

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• Gamma ray bursts
• General relativity
• Gravitation
• Gravitational waves
• Accretion disk & black-hole plasma