Precession of spherical orbits and observational constraints on black hole parameters from the jet of M87*

Recent observations of the jet precession of M87* provide a new opportunity to probe strong gravity effects and the spacetime geometry around supermassive black holes. In particular, the observed precession period strongly suggests the presence of a rotating black hole surrounded by a tilted accretion disk, making jet precession a promising astrophysical probe of relativistic orbital dynamics. In this work, we investigate the Lense–Thirring precession of spherical orbits in rotating black hole spacetimes and explore its implications for tilted accretion disks and jet dynamics. Using the Hamiltonian formalism, we derive the equations of motion for spherical orbits in general stationary axisymmetric spacetimes and apply the formalism to Kerr–Newman and Kerr–Taub–NUT black holes.

We show that both the black hole charge and the NUT charge significantly affect the precession of spherical orbits. In particular, the black hole charge suppresses the precession angular velocity, whereas the NUT charge enhances it and further breaks the $\mathbb{Z}_2$ reflection symmetry of the orbits, leading to asymmetric orbital trajectories with respect to the equatorial plane. By modeling the motion of particles near the warp radius of a tilted accretion disk with spherical orbits, we use the observed jet precession of M87* to constrain the black hole parameter space, including the spin, charge, NUT charge, and warp radius, and discuss their implications for tilted accretion disk structures and possible naked singularity scenarios.

These results suggest that jet precession observations can provide useful insight into nontrivial black hole parameters and the underlying spacetime symmetry structure.