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

TL;DR

The paper investigates how a dynamically significant magnetic field, encoded in the Kerr-Bertotti-Robinson spacetime, reshapes spherical orbits and their Lense–Thirring precession using a Hamiltonian approach for non-separable timelike geodesics. It reveals a rich orbital topology, including ISSO, MSSO, and CSO, with a magnetic-field–induced swallowtail structure and a critical field beyond which radially stable spherical orbits disappear. By matching the observed M87* jet precession period, the authors derive a robust upper bound on the magnetic field and connect this to the warp radius and inner-disk geometry, independent of the shadow. Overall, jet precession emerges as a precise, complementary probe of magnetized black-hole spacetimes in the strong gravity regime.

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.

Figures (9)

• Figure 1: Contour plot of the outer event horizon radius $r_+/M$ in the KBR spacetime as a function of the dimensionless black hole spin $a/M$ and magnetic field parameter $BM$. The color bar indicates the value of $r_+/M$, and the contour lines represent constant horizon radius. In the Kerr limit ($B=0$), the standard Kerr horizon structure is recovered.
• Figure 2: Visualization of spherical orbits and their LT precession in the KBR spacetime for fixed parameters $a/M=0.9$ and $BM=0.01$. (a) Families of the spherical orbits with different inclination angles $\zeta=\pi/6,\ \pi/4,\ \pi/3$ (in magenta, blue, and red colors), shown together with the equatorial cyan ring. Solid (dashed) curves correspond to the prograde (retrograde) motions. (b) A representative inclined spherical orbit with $\zeta=\pi/4$, illustrating the secular precession of the orbital plane about the spin axis when described with respect to the. Boyer-Lindquist coordinates. (c) Projection of the same orbit onto the plane perpendicular to the spin axis, showing a non-closed trajectory due to the cumulative LT precession. (d) The same trajectory represented in a uniformly rotating reference frame with angular velocity equal to the mean precession rate, in which the underlying closed trajectory is recovered. These figures illustrate the geometric origin of the precession frequency $\omega_{\rm LT}$ defined in Sec. \ref{['sec3']}.
• Figure 3: Energy-angular momentum ($E_s$, $L_s$) diagrams for the spherical orbits in the KBR spacetime with fixed spin $a/M=0.9$ and inclination angle $\zeta=1.25^\circ$. Each curve is. parametrized by the orbital radius $r_0$. The curves originate near the outer event horizon at $E_s>1$ and evolve as $r_0$ increases. (a) Prograde spherical orbits. (b) Retrograde spherical orbits.
• Figure 4: Energy and angular momentum of spherical orbits as functions of the orbital radius $r_0/M$ in the KBR spacetime with the inclination angle $\zeta = 1.25^\circ$. The upper (lower) row shows prograde (retrograde) orbits. Solid and dashed curves represent black hole spins $a/M = 0.3$ and $0.9$, respectively, while different colors denote different magnetic field strengths $B$ as indicated. Local extrema of $E_s(r_0)$ or $L_s(r_0)$ signal transitions in radial stability and identify characteristic spherical orbits, including the ISSOs and the MSSOs. These extrema provide the dynamical origin of the cusp and swallowtail structures observed in the $(E_s, L_s)$ space shown in Fig. \ref{['spoEL']}. (a) $E_s(r_0)$ for prograde orbits. (b) $L_s(r_0)$ for prograde orbits. (c) $E_s(r_0)$ for retrograde orbits. (d) $L_s(r_0)$ for retrograde orbits.
• Figure 5: Contour plots of the radius $r_{\mathrm{ISSO}}/M$ of ISSOs in the $(a/M, BM)$ parameter space for a fixed inclination angle $\zeta = 1.25^\circ$. The color bar indicates the dimensionless radius $r_{\mathrm{ISSO}}/M$. These contours illustrate how the location of the ISSOs varies across the parameter space and provide the lower bound for the warp radius $r_{\mathrm{w}}$ used in the disk precession analysis of Sec. \ref{['sec4']}. (a) Prograde orbits. (b) Retrograde orbits.