Orbital dynamics and precession in magnetized Kerr spacetime

TL;DR

The paper addresses neutral-particle dynamics in the magnetized Kerr (MKBH) spacetime, an exact Einstein–Maxwell solution that embeds a uniform external magnetic field into the Kerr geometry. It derives the equatorial effective potential and exact/perturbative expressions for the fundamental frequencies $\Omega_\phi$, $\Omega_r$, and $\Omega_\theta$, along with their precession counterparts $\Omega_{\text{per}}$ and $\Omega_{\text{nod}}$, and identifies a critical field $B_{\text{cr}}$ beyond which circular orbits are forbidden. A new OSCO (outmost stable circular orbit) emerges from the Melvin-type asymptotics, confining stable motion to a finite radial domain, while a magnetically induced reversal of $\Omega_{\text{per}}$ appears within a finite range of radii. These results illuminate how magnetic curvature modifies strong-field geodesics and offer a self-consistent framework for interpreting QPO phenomenology and magnetization imprints in precision timing around compact objects.

Abstract

We study the orbital structure and precession dynamics of neutral test particles in the magnetized Kerr black hole (MKBH) spacetime-an exact electrovacuum solution of the Einstein-Maxwell equations that self-consistently incorporates the curvature effects of an external magnetic field. This geometry allows a unified treatment of gravitational and magnetic influences across weak to ultra-strong regimes. The analysis reveals a critical magnetic field strength above which no circular geodesics, timelike or null, can exist, establishing an upper magnetic bound for orbital motion. For subcritical fields, the photon circular orbit admits two real roots, the outer of which defines an outermost stable circular orbit (OSCO), complementing the conventional innermost stable circular orbit (ISCO) and confining stable motion within a finite radial domain. Exact expressions for the orbital, radial, and vertical epicyclic frequencies, and their associated precession rates, show substantial deviations from Kerr behavior, including a magnetically induced reversal of periastron precession within a finite radial range. For astrophysically relevant magnetic field strengths, the retrograde precession could be observable at large radii around astrophysical BHs, offering a potential diagnostic of large-scale magnetization. These findings highlight the geometric influence of magnetic curvature on strong-field dynamics, providing a self-consistent framework to interpret quasi-periodic oscillation phenomenology and potential magnetic imprints in precision timing observations of compact objects.

Figures (8)

• Figure 1: The potential functions $V_+(r)$ (solid curves) and $V_-(r)$ (dashed curves) for prograde equatorial orbits in the MKBH spacetime, with spin parameters (a) $a_* = 0.1$ and (b) $a_* = 0.9$ for different magnetic field strengths $B$ are plotted. See Sec. \ref{['sec:veffmagkerr']} for details.
• Figure 2: CPO radius $r (M)$ as a function of $B (M^{-1})$ for various spin parameter $a_*$. Turning point ($\equiv B_\text{cr}$) of each curve marks the critical field strength beyond which no circular orbits exist. See Sec. \ref{['sec:CPO']} for further details.
• Figure 3: Parameter space for stable circular orbits in the equatorial plane. The solid curve divides the $B-a_*$ plane into regions where circular orbits are permitted (left) and forbidden (right). The endpoints of the curve are located at $(a_*,B) \sim (0, 0.189 M^{-1})$ and $(1, 0.556 M^{-1})$. See Sec. \ref{['sec:CPO']} for further details.
• Figure 4: $r$ (in $M$) as a function of $B$ (in $M^{-1}$) for MKBH with different spin parameters $a_*$. For each value of $a_*$, the CPO equation yields two branches, with the outer one identified as OSCO. We have drawn ISCO for reference. At the critical field $B_{\text{cr}}$ all three coincide at point P. Beyond this point, no circular orbits—timelike or null—are allowed. See Sec. \ref{['sec:OSCO']} for details.
• Figure 5: $r_{\text{ISCO}}$ (in units of $M$) as a function of $B$ (in $M^{-1}$) for varying spin parameter $a_*$. The ISCO radius reaches a maximum at $B = 0$ and decreases monotonically with increasing $B$, except for the extremal case. See Sec. \ref{['subsec:ISCO']} for further details