Magnetic field effects on spherical orbit in Kerr-Bertotti-Robinson spacetime: constraints from jet precession of M87*

Abstract: The recently reported precession period of about $11.24$ years of the M87* jet provides a sensitive probe of strong field gravity and the electromagnetic environment in the immediate vicinity of supermassive black holes. In this work, we study the precession of the spherical orbit in the Kerr-Bertotti-Robinson geometry describing a rotating black hole immersed in a uniform electromagnetic field. Although the timelike geodesics is non-separable, we develop a Hamiltonian approach to investigate the spherical orbits. For sufficiently strong magnetic fields, the study shows that the spherical orbits can only exist within a finite radial range for given orbital inclination. Requiring the existence of the spherical orbits, we obtain an upper bound of the magnetic field, i.e., $B<0.33 M^{-1}$ for prograde and $B<0.0165 M^{-1}$ for retrograde motion. Furthermore, imposing the observed jet precession period, we obtain a significantly tighter constraint, $B\lesssim 0.0145 M^{-1}$, providing a new constrain on the magnetic field of M87* independent of the shadow. Our results provide unified constraints on the parameters of the KBR black hole and demonstrate that the jet precession offers a robust and complementary probe of magnetized black holes in the strong gravity regime.