Existence and multiplicity results for massive particles trajectories in a universe with boundary

Details Existence and multiplicity results for massive particles trajectories in a universe with boundary Existence and multiplicity results for massive particles trajectories in a universe with boundary

Nov 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999jmp....40.5835g&link_type=abstract

Journal of Mathematical Physics, Volume 40, Issue 11, pp. 5835-5848 (1999).

Mathematics

Mathematical Physics

1

Fundamental Problems And General Formalism, Relativity And Gravitation

Scientific paper

In an open time-convex region Λ of a strongly causal Lorentzian manifold (M,g), we consider an event p and a timelike, injective curve γ. We look for geodesics connecting p and γ in Λ and satisfying the conservation law g(z)[ż,ż]=-E for a fixed E>0. It is already known that such geodesics are the stationary points of the arrival time functional τ. Our main result is to prove the existence of a decreasing flow for τ, by means of a shortening procedure. This makes possible to apply to τ global variational methods obtaining existence and multiplicity results (using the Ljusternik-Schnirelmann category theory) and also to develop a Morse theory.

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