Spinning test particles in the γ spacetime

Abstract

We consider the motion of spinning particles in the field of a well-known vacuum static axially-symmetric spacetime, known as γ metric, that can be interpreted as a generalization of the Schwarzschild manifold to include prolate or oblate deformations. We derive the equations of motion for spinning test particles by using the Mathisson-Papapetrou-Dixon equations together with the Tulczyjew spin-supplementary condition and restricting the motion to the equatorial plane. We determine the limit imposed by super-luminal velocity for the spin of the particle located at the innermost stable circular orbits (ISCOs). We show that the particles on ISCO of the prolate γ spacetime are allowed to have higher spin than the corresponding ones in the oblate case. We determine the value of the ISCO radius depending on the signature of the spin-angular momentum, s-L relation, and show that the value of the ISCO with respect to the nonspinning case is bigger for sL < 0 and smaller for sL > 0. The results may be relevant for determining the properties of accretion disks and constraining the allowed values of quadrupole moments of astrophysical black hole candidates.