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

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

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

CYK Tensors, Maxwell Field and Conserved Quantities for Spin-2 Field

Starting from an important application of Conformal Yano--Killing tensors for the existence of global charges in gravity, some new observations at \scri^+ are given. They allow to define asymptotic charges (at future null infinity) in terms of the Weyl tensor together with their fluxes through \scri^+. It occurs that some of them play a role of obstructions for the existence of angular momentum. Moreover, new relations between solutions of the Maxwell equations and the spin-2 field are given. They are used in the construction of new conserved quantities which are quadratic in terms of the Weyl tensor. The obtained formulae are similar to the functionals obtained from the Bel--Robinson tensor.Comment: 20 pages, LaTe

Mathisson-Papapetrou-Dixon equations in the Schwarzschild and Kerr backgrounds

A new representation, which does not contain the third-order derivatives of the coordinates, of the exact Mathisson-Papapetrou-Dixon equations, describing the motion of a spinning test particle, is obtained under the assumption of the Mathisson-Pirani condition in a Kerr background. For this purpose the integrals of energy and angular momentum of the spinning particle as well as a differential relationship following from the Mathisson-Papapetrou-Dixon equations are used. The form of these equations is adapted for their computer integration with the aim to investigate the influence of the spin-curvature interaction on the particle's behavior in the gravitational field without restrictions on its velocity and spin orientation. Some numerical examples for a Schwarzschild background are presented.Comment: 21 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1105.240

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

Ethnicity and baseline symptomatology in patients with an At Risk Mental State for psychosis

Ethnicity has been associated with different incidence rates and different symptom profiles in young patients with psychotic-like disorders. No studies so far have examined the effect of ethnicity on symptoms in people with an At Risk Mental State (ARMS). In this cross-sectional study, we analysed the relationship between ethnicity and baseline data on the severity of psychopathology scores in 201 help-seeking patients who met the ARMS criteria and agreed to participate in the Dutch Early Detection and Intervention (EDIE-NL) trial. Eighty-seven of these patients had a non-Dutch ethnicity. We explored the possible mediating role of ethnic identity. Higher rates of negative symptoms, and of anhedonia in particular, were found in the ethnic minority group. This result could be attributed mainly to the Moroccan-Dutch and Turkish-Dutch subgroups, who also presented with more depression symptoms when the groups were examined separately. The ethnic minority group displayed a lower level of ethnic group identity compared to the immigrants of the International Comparative Study of Ethnocultural Youth (ICSEY). Ethnic identity was inversely related to symptoms in the Moroccan-Dutch patient group. The prevalence of more severe negative symptoms and depression symptoms in ethnic minority groups deserves more attention, as the experience of attenuated positive symptoms when accompanied by negative symptoms or distress has proven to be predictive for transition to a first psychotic episod

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