1,721,088 research outputs found
Periodic trajectories on stationary Lorentzian manifolds
No full textAn existence and multiplicity result for periodic trajectories on stationary Lorentzian manifolds, possibly with boundary, whose proof is based on a Morse theory approach is presented. A Lorentzian manifold is a smooth connected finite-dimensional manifold M equipped with a (0,2) tensor field g such that for any z∈M g(z) [·,·] is a nondegenerate symmetric bilinear form on the tangent space TzM having exactly one negative eigenvalue. Moreover, relativistic spacetimes are a particular class of Lorentzian manifolds of dimension fou
Trajectories Connecting Two Events of a Lorentzian Manifold in the Presence of a Vector Field
No full textConvexity conditions on the boundary of a stationary spacetime and applications
No full textWe deal with the convexity of the boundary of a standard stationary spacetime L =
M × R. We obtain a characterization of this notion by means of Riemannian conditions
involving a potential plus a magnetic field on M , where both are linked to the coefficients
of the metric. Natural applications of our results concern geodesics having a prescribed
parametrization proportional to the arc length, joining a point to a line and periodic,
on non-complete manifolds, and in particular on Kerr spacetime
Orthogonal trajectories on Riemannian manifolds and applications to Plane Wave type spacetimes
No full textWe present a result on trajectories of a Lagrangian system joining two given submanifolds of a
Riemannian manifold, under the action of an unbounded potential. As an application, we consider geodesics
in a class of semi-Riemannian manifolds, the Plane Wave type spacetimes
Trajectories of a charge in a magnetic field on Riemannian manifolds with boundary
No full textWe prove an existence result for trajectories of classical particles accelerated
by a potential and a magnetic field on a non–complete Riemannian manifold M . Both the
potential and the magnetic field may be not bounded and have critical growth. We state
a suitable convexity assumption involving the magnetic field in order to prove that the
support of each trajectory is entirely contained in M
Timelike spatially closed trajectories under a potential on spitting Lorentzian manifolds
No full textWe study the periodic motions of a relativistic particle submitted to the action of an external potential . We consider on a wide class of Lorentzian manifolds, timelike solutions of a differential equation depending on closed in the spatial component and satisfying a Dirichlet condition in the temporal one. We prove a multiplicity result for the critical points of the (strongly indefinite) functional associated to the problem by means of a saddle type theorem based on the notion of relative category. The periodicity of the problem, the non--compactness of the manifold and the fact that some assumptions involving the relative category fail make necessary to use a suitable penalization for the action functional and a Galerkin approximation
Trajectories joining two submanifolds under the action of gravitational and electromagnetic fields on static spacetimes
No full textRemarks on some variational problems on non-complete manifolds
No full textWe shall review recent results obtained in the study of some periodic variational problems on Riemannian and Lorentzian manifolds with boundary. Firstly we shall analyze the existence. of closed geodesics on a Riemannian manifold (M, (R))Then we shall deal respectively with periodic trajectories and periodic trajectories under a vectorial potential on stationary Lorentz manifolds. Finally, we discuss the different hypotheses on the boundary, and state some open questions
Geodesics with prescribed energy on static Lorentzian manifolds with convex boundary, J. Geom. Phys. 32 (2000), 293-310
No full textTimelike spatially closed trajectories under a potential on splitting Lorentzian manifolds
No full textWe study the periodic motions of a relativistic particle submitted
to the action of an external potential V . On a wide class of Lorentzian manifolds,
we find timelike solutions of a differential equation (depending on V ) closed in the
spatial component and satisfying a Dirichlet condition in the temporal one. We
prove a multiplicity result for the critical points of the (strongly indefinite) functional
associated to the problem, using a saddle type theorem based on the notion of relative
category. The periodicity of the problem, the non–compactness of the manifold and
the lack of some assumptions involving the relative category make necessary to use a
suitable penalization scheme and a Galerkin approximation
- …
