Equations of motion of a spinning relativistic particle in external fields

Abstract

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The correct account for the spin influence on the particle trajectory is obtained with the noncovariant description of spin. Concrete calculations are performed up to second order in spin included. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a specific spin effect in general relativity. It is demonstrated that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals to unity (as well as for the charged Kerr hole the gyromagnetic ratio equals to two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

“…The same conclusion follows from comparison of equations of motion of the two formulations [10]. As we saw in Section 5.1, the expression (188) has very strong experimental support.…”

“…As we saw in Section 5.1, the expression (188) has very strong experimental support. The question why a covariant formalism does not lead directly to the correct result has been raised in 1926 [13] and remains under discussion to date [10,36,90]. Following the work [31], in Section 11 we show that the vector model provides an answer to this question on a pure classical ground, without appeal to the Thomas precession, Dirac equation, or Foldy-Wouthuysen transformation.…”

“…The equations are necessary for current applications of general relativity on various spacetime scales: for analysis of Lense-Thirring precession [9], for accounting spin effects in compact binaries and rotating black holes [10,11], and in discussion of cosmological problems; see [12] and references therein. Closely related problem consists in establishing classical equations that could mimic quantum mechanics of an elementary particle with spin in a semiclassical approximation [13][14][15][16][17].…”

Equivalence principle and experimental tests of gravitational spin effects

“…[4,5,8] and references therein). Evidently, this coupling given in the form of S ·g (g is the acceleration) contradicts to the theory [4,6] and violates both the CP invariance and the relation predicting the absence of the gravitoelectric dipole moment [1]. Therefore, the negative result of realized experiments imposes some restrictions not only on the spin-gravity coupling but also on the gravitoelectric dipole moment.…”

“…These properties of spin-gravity interaction were explored in the number of theoretical papers and suggestions for experiments (see Refs. [4,5,6] and references therein). There are also some evidences supporting the conjecture [7] that the absence of the AGM is valid separately for quarks and gluons in the nucleon, which may be related to the phenomena of confinement and spontaneous chiral symmetry breaking.…”