Motions and world-line deviations in Einstein-Maxwell theory

We examine the motion of charged particles in gravitational and electro-magnetic background fields. We study in particular the deviation of world lines, describing the relative acceleration between particles on different space-time trajectories. Two special cases of background fields are considered in detail: (a) pp-waves, a combination of gravitational and electro-magnetic polarized plane waves travelling in the same direction; (b) the Reissner-Nordstr{\o}m solution. We perform a non-trivial check by computing the precession of the periastron for a charged particle in the Reissner-Nordstr{\o}m geometry both directly by solving the geodesic equation, and using the world-line deviation equation. The results agree to the order of approximation considered.Comment: 23 pages, no figure

Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime

In spacetimes admitting Yano tensors the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank two, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors.Comment: 1+32 pages, no figures. Accepted for publication on Classical and Quantum Gravity. New title and abstract. Some material has been moved to the Appendix. Concrete formulas for Yano tensors on some special holonomy manifolds have been provided. Some corrections included, bibliography enlarge

Generalized Killing equations and Taub-NUT spinning space

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Simple solutions of the homogeneous part of these equations are expressed in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional euclidean Taub-NUT manifold.Comment: 10 pages, late

Equations of Motion of Spinning Relativistic Particle in Electromagnetic and Gravitational Fields

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 noncovariant spin formalism is crucial for the correct description of the influence of the spin on the particle trajectory. We show that the true coordinate of a relativistic spinning particle is its naive, common coordinate \r. 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 shown that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals unity (just as for the charged Kerr hole the gyromagnetic ratio equals two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.Comment: 32 pages, latex, Plenary talk at the Fairbank Meeting on the Lense--Thirring Effect, Rome-Pescara, 29/6-4/7 199

Equations of Motion of Spinning Relativistic Particle in External Fields

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.Comment: 22 pages, latex, no figure

Stability of circular orbits of spinning particles in Schwarzschild-like space-times

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space-time leading to the conclusion that the orbits are stable.Comment: eps figures, submitted to General Relativity and Gravitatio

Massless geodesics in AdS5×Y(p,q)AdS_5\times Y(p,q) as a superintegrable system

A Carter like constant for the geodesic motion in the $Y(p,q)$ Einstein-Sasaki geometries is presented. This constant is functionally independent with respect to the five known constants for the geometry. Since the geometry is five dimensional and the number of independent constants of motion is at least six, the geodesic equations are superintegrable. We point out that this result applies to the configuration of massless geodesic in $AdS_5\times Y(p,q)$ studied by Benvenuti and Kruczenski, which are matched to long BPS operators in the dual N=1 supersymmetric gauge theory.Comment: 20 pages, no figures. Small misprint is corrected in the Killing-Yano tensor. No change in any result or conclusion