TY - JOUR

T1 - Gravitational Magnus effect

AU - Costa, L. Filipe O.

AU - Franco, Rita

AU - Cardoso, Vitor

PY - 2018/7/13

Y1 - 2018/7/13

N2 - 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-Lemaitre-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.

AB - 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-Lemaitre-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.

KW - POTENTIAL-DENSITY PAIRS

KW - RELATIVISTIC DISKS

KW - BLACK-HOLES

KW - SPINNING SPHERE

KW - FREE MOTION

KW - FORCE

KW - RINGS

KW - INTEGRABILITY

KW - PRECESSION

KW - MOMENTUM

U2 - 10.1103/PhysRevD.98.024026

DO - 10.1103/PhysRevD.98.024026

M3 - Journal article

VL - 98

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 2

M1 - 024026

ER -