For twisted particles in arbitrary gravitational fields, the problems of the rotation of intrinsic orbital angular momentum and the orbital Hall effect are solved in the general case. We need not use the Maxwell equations in curved spacetimes for a description of twisted photons. The exact general equation rigorously defining the orbital-angular-momentum dynamics in any Riemannian spacetimes is derived. The general description of different manifestations of the orbital Hall effect for any twisted particles is also presented. Our short analysis shows that the results obtained can find important practical applications.

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• Cosmic rays & astroparticles
• General relativity
• Particle astrophysics