ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
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)[z(overdot),z(overdot)]=−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. © 1999 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.533058
Permalink