Geodesic Motion in Spinning Spaces

In this paper the generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We study the geodesic motion of the pseudo-classical spinning particles in the spacetime produced by an idealized cosmic string and the non-extreme stationary axisymmetric black hole spacetime. The bound state orbits in a plane are discussed. We also show, for a conical spacetime and the Kerr spacetime, that the geodesic motion of spinning particles is different.     

Geodesic Motion in Spinning Spaces

In this paper the generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We study the geodesic motion of the pseudo-classical spinning particles in the spacetime produced by an idealized cosmic string and the non-extreme stationary axisymmetric black hole spacetime. The bound state orbits in a plane are discussed. We also show, for a conical spacetime and the Kerr spacetime, that the geodesic motion of spinning particles is different.     

Spinning Particles in Reissner-Nordström-de Sitter Spacetime

We study the geodesic motion of pseudo-classical spinning particles in the Reissner-Nordström-de Sitter spacetime. We investigate the generalized Killing equations for spinning space and derive the constants of motion in terms of the solutions of these equations. We discuss bound state orbits in a plane.     

Quasi-Maxwell interpretation of the spin–curvature coupling

We write the Mathisson-Papapetrou equations of motion for a spinning particle in a stationary spacetime using the quasi-Maxwell formalism and give an interpretation of the coupling between spin and curvature. The formalism is then used to compute equilibrium positions for spinning particles in the NUT spacetime. This work was partially supported by FCT/POCTI/FEDER.     

Motions in Taub-NUT–de Sitter spinning spacetime

We investigate the geodesic motion of pseudo-classical spinning particles in the Taub-NUT–de Sitter spacetime. We obtain the conserved quantities from the solutions of the generalized Killing equations for spinning spaces. Applying the formalism the motion of a pseudo-classical Dirac fermion is analyzed on a cone and plane.     

Spinning Test Particles as Locally Nonrotating Observers in Kerr Spacetime

We derive a class of exact solutions of Mathisson-Papapetrou equations of motion for spinning test particles. The world lines of the particles are those of the so-called locally non-rotating observers in Kerr spacetime.     

Stationary spinning strings and symmetries of classical spacetimes

We explore the symmetries of classical stationary spacetimes in terms of the dynamics of a spinning string described by a worldsheet supersymmetric action. We show that for stationary configurations of the string, the action reduces to that for a pseudo-classical spinning point particle in an effective space, which is a conformally scaled quotient space of the original spacetime. As an example, we consider the stationary spinning string in the Kerr–Newman spacetime, whose motion is equivalent to that of the spinning point particle in the three-dimensional effective space. We present the Killing tensor as well as the spin-valued Killing vector of this space. However, the nongeneric supersymmetry corresponding to the Killing–Yano tensor of the Kerr–Newman spacetime is lost in the effective space.     

Spin-geodesic deviations in the Schwarzschild spacetime

The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson–Papapetrou–Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin–curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin–curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.     

Massless spinning test particles in a gravitational field

The classical equations of motion of a massless spinning test particle are derived as a limiting case of Mathisson-Papapetrou equations. It is shown that when a particular supplementary condition is assumed the particle follows a null geodesic and the spin is either parallel or antiparallel to the direction of motion. Moreover, the helicity is conserved in an orientable spacetime. The equations of the propagation of the momentum vector and the spin tensor along the trajectory are given and further implications of the solution are discussed.     

Constrained dynamics of an anomalous (g≠2) relativistic spinning particle in electromagnetic background

In this paper we have considered the dynamics of an anomalous (g≠2) charged relativistic spinning particle in the presence of an external electromagnetic field. A constraint analysis is done and the complete set of Dirac brackets are provided that generate the canonical Lorentz algebra and dynamics through Hamiltonian equations of motion. The spin-induced effective curvature of spacetime and its possible connection with Analogue Gravity models are commented upon.     

Spinning Particles in NUT–Reissner–Nordstrom Space–Time

We study the geodesic motion of pseudo-classical spinning particles in the NUT–Reissner–Nordstrom space–time. We investigate the generalized Killing equations for spinning space and derive the constants of the motion in terms of the solutions of these equations. We give an analysis of the motion on a cone and on a plane.     

On the motion of particles and strings,presymplectic mechanics,and the variational bicomplex

Examples of equations of motion in classical relativistic mechanics are studied: the equations of motion of a charged spinning particle moving in a space-time (with or without torsion) in the presence of an electromagnetic field are derived via Souriau presymplectic reduction. Then, the extension of Souriaus ideas to Lagrangian field theory due to Witten, Crnkovi, Zuckerman is reviewed using the variational bicomplex, the basic properties of the Lund–Regge equations describing the motion of a string interacting with a scalar field and moving in Minkowski spacetime are recalled, and a symplectic structure for their space of solutions is found.This revised version was published online in April 2005. The publishing date was inserted.     

Symmetries and Motions in NUT-Taub Spinning Space

We review the geodesic motion of pseudo-classical spinning particles in curved space. We describe the generalized Killing equations for spinning spaces and express the constants of motion. We apply the formalism to solve for the motion of a pseudo-classical Dirac fermion in NUT-Taub spinning space and analyze the motion on a cone and on a plane.     

Charged Taub-NUT-de Sitter spacetime in DGP braneworld and its thermodynamics

We study a charged Taub-NUT spacetime solution in the Dvali-Gabadadze-Porrati (DGP) brane. We show that the Reissner-Nordstrom-Taub-NUT-de Sitter solution of Einstein-Maxwell gravity solves the corresponding equations of motion, where the cosmological constant is related to the cross-over scale in the DGP model. Following the approach by Teitelboim in discussing the thermodynamics of de Sitter spacetime and the proposal by Wu et al. for a conserved charge associated with the NUT parameter, we obtain the generalized Smarr mass formula and the first law of thermodynamics of the spacetime.     

Bradyon-luxon symmetry

We propose a spacetime scheme representing the union of the real and non-real spacetime as a possible geometrical framework for Caldirola’s idea, that the bradyonic motion can be regarded as a light-like motion in an additional extra space. The playground of all physical processes is the union space. However, the physical processes in union space are differently projected on the real and non-real spacetime. The waves linked with luxons in union space are projected on the real spacetime so that they propagate here always with the velocity of light. The waves linked with bradyons in union space are projected on the non-real spacetime so that they propagate here with the velocity of light. The wave linked with a bradyon in union space, which is projected on the real spacetime, is here described by the Schroedinger and Dirac equations. There is proposed a symmetry which demands that the physical world is in its law the same whether it is seen from real or non-real spacetime. We discuss some consequences of this symmetry in the theory of elementary particles.     

Toward a Finite-Dimensional Formulation of Quantum Field Theory

Rules of quantization and equations of motion for a finite-dimensional formulation of quantum field theory are proposed which fulfill the following properties: (a) Both the rules of quantization and the equations of motion are covariant; (b) the equations of evolution are second order in derivatives and first order in derivatives of the spacetime coordinates; and (c) these rules of quantization and equations of motion lead to the usual (canonical) rules of quantization and the (Schrödinger) equation of motion of quantum mechanics in the particular case of mechanical systems. We also comment briefly on further steps to fully develop a satisfactory quantum field theory and the difficuties which may be encountered when doing so.     

Geodesic Motion on Extended Taub-NUT Spinning Space

In this paper we investigate the geodesic motion of the pseudo-classical spinning particle for the extended Taub-NUT metric. The generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We find only two types of extended Taub-NUT metrics with Kepler type symmetry admitting Killing-Yano tensors. The solutions for the lowest components of generalized Killing equations are presented for a particular form of extended Taub-NUT metric.     

Perturbation of pulsating strings

We discuss semiclassical quantization of circular pulsating strings in \( \text {AdS}_3 \times \text {S}^3 \) background with and without the Neveu-Schwarz–Neveu-Schwarz (NS–NS) flux. We find the equations of motion corresponding to the quadratic action in bosonic sector in terms of scalar quantities and invariants of the geometry. The general equations for studying physical perturbations along the string in an arbitrary curved spacetime are written down using covariant formalism. We discuss the stability of these string configurations by studying the solutions of the linearized perturbed equations of motion.     

The Spinning and Curving of Spacetime: The Electromagnetic and Gravitational Fields in the Evans Field Theory

The unification of the gravitational and electromagnetic fields achieved geometrically in the generally covariant unified field theory of Evans implies that electromagnetism is the spinning of spacetime and gravitation is the curving of spacetime. The homogeneous unified field equation of Evans is a balance of spacetime spin and curvature and governs the influence of electromagnetism on gravitation using the first Bianchi identity of differential geometry. The second Bianchi identity of differential geometry is shown to lead to the conservation law of the Evans unified field, and also to a generalization of the Einstein field equation for the unified field. Rigorous mathematical proofs are given in appendices of the four equations of differential geometry which are the cornerstones of the Evans unified field theory: the first and second Maurer-Cartan structure relations and the first and second Bianchi identities. As an example of the theory, the origin of wavenumber and frequency is traced to elements of the torsion tensor of spinning spacetime.