1,721,449 research outputs found
Trajectories of charged particles in a region of a stationary spacetime
No full textWe study the trajectories for relativistic particles under the action of gravitational and electromagnetic stationary fields. We show how the topology of the spacetime influences the number of such trajectories. The results are applied to the Reissner-Nordstrom spacetime
Trajectories for relativistic particles under the action of an electromagnetic field in a stationary space-time
No full textTrajectories for relativistic particles were studied under the effect of an electromagnetic field in a stationary space-time. Particle was described by a smooth timelike curve 'wordline' in a space-time. A suitable class of curves on a Lorentzian manifold was given by a smooth curve, geodesic. Geodesics satisfy a variational principle. The number of nontrivial timelike periodic trajectories were found to be large for the assumption that the number of points in which the vector field vanishes was finit
The Avez-Seifert theorem for the relativistic Lorentz force equation
No full textIn this paper we prove an extension of the Avez-Seifert theorem to the relativistic Lorentz force equation. Let (M,g) be a globally hyperbolic space-time, F an exact 2-form on M representing the electromagnetic field, (F) over cap the Lorentz force associated to F, and q a charge for a test particle. Let p(0) and p(1) be two chronologically related points on M, then there exists a future-pointing timelike solution of the Lorentz force equation D-s(z)over dot=q (F) over cap (z)[(z)over dot], connecting p(0) and p(1). (C) 2004 American Institute of Physics
On a Fermat principle in General Relativity. A Lusternik-Schirelmenn theory for light rays
No full textOn the number of solutions for the two-point boundary value problem on Riemannian manifolds
No full textWe study the solutions joining two fixed points of a time-independent dynamical system on a Riemannian manifold (M, g) from an enumerative point of view. We prove a finiteness result for solutions joining two points p, q is an element of M that are non-conjugate in a suitable sense, under the assumption that (M, g) admits a non-trivial convex function. We discuss in some detail the notion of conjugacy induced by a general dynamical system on a Riemannian manifold. Using techniques of infinite dimensional Morse theory on Hilbert manifolds we also prove that, under generic circumstances, the number of solutions joining two fixed points is odd. We present some examples where our theory applie
Causal properties of Kaluza-Klein metrics
No full textWe present some global properties of Kaluza-Klein metrics. We state that the Kaluza-Klein metrics associated to globally hyperbolic spacetimes are globally hyperbolic. Applications to the solutions of the relativistic Lorentz equation are shown. (C) 2004 Elsevier Ltd. All rights reserved
A Fermat principle for stationary space-times and applications to light rays on Lorentzian manifolds
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