Gravitational Magnus effect

Abstract

It is well known that a spinning body moving in a fluid suffers a force orthogonal to its velocity and rotation axis --- it is called the Magnus effect. Recent simulations of spinning black holes and (indirect) theoretical predictions, suggest that a somewhat analogous effect may occur for purely gravitational phenomena. The magnitude and precise direction of this "gravitational Magnus effect" is still the subject of debate. Starting from the rigorous equations of motion for spinning bodies in General Relativity (Mathisson-Papapetrou equations), we show that indeed such an effect takes place and is a fundamental part of the spin-curvature force. The effect arises whenever there is a current of mass/energy, non-parallel to a body's spin. We compute the effect explicitly for some astrophysical systems of interest: a galactic dark matter halo, a black hole accretion disk, and the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. It is seen to lead to secular orbital precessions potentially observable by future astrometric experiments and gravitational-wave detectors. Finally, we consider also the reciprocal problem: the "force" exerted by the body on the surrounding matter, and show that (from this perspective) the effect is due to the body's gravitomagnetic field. We compute it rigorously, showing the matching with its reciprocal, and clarifying common misconceptions in the literature regarding the action-reaction law in post-Newtonian gravity.

arXiv comment28 pages, 9 figures. References added, matches the final published version

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• General relativistic magnetized Bondi-Hoyle-Lyttleton accretion with a spin-field misalignment: Jet nutation, polarity reversals, and Magnus drag
• Reference frames in General Relativity and the galactic rotation curves
• Poynting vector, super-Poynting vector, and principal observers in electromagnetism and general relativity
• Mass and spin coevolution of black holes inspiralling through dark matter
• Frame-dragging: meaning, myths, and misconceptions