Spinning test particles in a Kerr field -- I

Abstract

A B S T R A C TMathisson±Papapetrou equations are solved numerically to obtain trajectories of spinning test particles in (the meridional section of) the Kerr space±time. The supplementary conditions p s S ms 0 are used to close the system of equations. The results show that in principle a spin-curvature interaction may lead to considerable deviations from geodesic motion, although in astrophysical situations of interest probably no large spin effects can be expected for values of spin consistent with a pole±dipole test-particle approximation. However, a significant cumulative effect may occur, e.g. in the inspiral of a spinning particle on to a rotating compact body, that would modify gravitational waves generated by such a system. A thorough literature review is included in the paper.

Dynamics of quadrupolar bodies in a Schwarzschild spacetime

“…Examples of purely numerical studies of the full nonlinear equations can be found in Refs. [11][12][13][14][15][16]. The existence of analytic solutions is only allowed in special situations which are in general too restrictive to yield a complete description of the nongeodesic motion induced by the structure of the body; for instance, by constraining the path along Killing trajectories in highly symmetric spacetimes, e.g., circular orbits [17][18][19][20][21][22][23], also in the ultrarelativistic regime [24].…”

Test particle motion in modified gravity theories

“…In general relativity, a pole-dipole particle is described by the four-momentum and the tensor of spin, and the dynamics is governed by the Mathisson-Papapetrou equations [2,3]. Combining these equations with a proper supplementary condition, one gets a self-consistent set of equations for describing the motion of a pole-dipole particle in a given space-time, for example see [4][5][6][7][8]. The case in which both gravitational and electromagnetic fields are present and the particle is charged was studied by Dixon and Souriau [9,10].…”

Motion of a spinning particle in curved space-time

“…There are two complimentary approaches to the subject. Since the gravitating objects possess quasi-rigid rotation along with orbital motion, studies have aimed at keeping track of the centre of mass by using different supplementary conditions with in the Mathisson-Papapetrou model [1][2][3][4][5][6][7][8][9][10][11][12] . In practise, determining the overall motion of the body, by following a detailed microscopic description of a material body is often too complicated.…”