Dragging of inertial frames in the composed Kerr-Newman-orbiting-ring system

Abstract

The dragging of inertial frames by an orbiting object, a well known phenomenon in general relativity, implies that the horizon angular velocity ΩHBH-ring of a central black hole in a composed black-hole-orbiting-ring system is no longer related to its angular-momentum JH by the familiar vacuum functional relation ΩH(JH)=JH/Mα (here {M,α} are respectively the mass and normalized area of the central spinning black hole). Using a continuity argument, according to which the black-hole angular velocity changes smoothly during an adiabatic assimilation process of an orbiting ring, it has recently been revealed that the composed Kerr-ring system is characterized by the universal (that is, spin-independent) relation ΔΩH≡ΩHBH-ring(JH,JR,R→RH+)−ΩHKerr(JH)=JR/4M3, where {R,JR} are respectively the radius of the ring and its orbital angular momentum and RH is the horizon radius of the central Kerr black hole. This intriguing observation naturally raises the following physically interesting question: Does the physical quantity ΔΩH in a composed black-hole-orbiting-ring system is always characterized by the near-horizon functional relation ΔΩH=JR/4M3 which is independent of the spin (angular momentum) JH of the central black hole? In order to address this important question, in the present compact paper we explore the physical phenomenon of dragging of inertial frames by an orbiting ring in the composed Kerr-Newman-black-hole-orbiting-ring system. In particular, using analytical techniques, we reveal the fact that in this composed two-body (black-hole-ring) system the quantity ΔΩH has an explicit non-trivial functional dependence on the angular momentum JH of the central spinning black hole.