Completeness of trajectories of relativistic particles under stationary magnetic fields

الأصل · EN

The second order differential equation Dγ/dt(t) = Fᵧ₍ₜ₎(γ(t)) - ∇ V(γ(t)) on a Lorentzian manifold describes, in particular, the dynamics of particles under the action of a electromagnetic field F and a conservative force -∇ V. We provide a first study on the extendability of its solutions, by imposing some natural assumptions.