Equilibrium of a charged test particle with spin in the Kerr - Newman spacetime

Abstract

The equilibrium of a charged test particle with spin placed in the field of the Kerr - Newman metric is studied. This is an extension of the earlier work which considered a charged test particle without spin. Now, both the stationary equilibrium conditions resulting from the equations of motion and the spin dynamics equations have to be satisfied. Consequently, the criteria for the equilibrium are modified. They are investigated and compared with the results obtained in the spinless case.

Spinning test particles in a Kerr field -- I

“…The conditions were suggested by Mathisson (1937) (the idea had already been found in a special‐relativistic treatment by Lanczos 1929), and then used, e.g., by Pirani (1956), Schiff (1960), Taub (1964), Wilkins (1970), Mashhoon (1971), Omote (1973), Rasband (1973), Ray & Smalley (1982), Prasanna & Virbhadra (1989), Aguirregabiria et al (1996) and Apostolatos (1996) 3 . Whereas they seem to be the most natural conditions for massless particles (Mashhoon 1975; Bailyn & Ragusa 1977; Duval & Fliche 1978), in the massive case they lead to a possibility of unphysical helical motions (Weyssenhoff & Raabe 1947a,b) as an effective consequence of a non‐unique choice of the centre of mass (or ‘center of gravity’, Møller 1949) of the particle.…”

Equilibrium of a charged test particle in the Kerr - Newman spacetime: force analysis

“…The behaviour of these forces offers insight into the mechanism of equilibrium. In a recent paper we have studied the equilibrium of charged test particles with spin placed in the Kerr-Newman spacetimes [8].…”