Orbital dynamics and precession in magnetized Kerr spacetime

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 $$B_{\textrm{cr}}(a_*)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mtext>cr</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mmultiscripts> <mml:mi>a</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> <mml:mrow/> </mml:mmultiscripts> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> 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 ( $$\Omega _{\textrm{per}} &lt; 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mtext>per</mml:mtext> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ) 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.