A note on the boundary of a static Lorentzian manifold

Geodesics in stationary spacetimes and classical Lagrangian systems

“…Here we extend the results in [14], dealing with a larger interval of energies and the ones in [5], working on (standard) stationary spacetimes (as will be better clarified in Remark 9). More precisely, we shall prove in Section 3 the following theorem.…”

“…In last years, they have been widely studied. Among the results on (standard) stationary manifolds, we recall [14] for the case E = 0, [5] where, in the static case, a wider range of energies (E E 0 where E 0 is strictly negative, if β is bounded from above) is considered and [24] where the same problem is analyzed in the causal cases, by geometric methods. For further results in the causal cases, on more general classes of manifolds, we recall also [15][16][17].…”

Trajectories under a vectorial potential on stationary manifolds

“…In [3], it has been proved that the previous definition is equivalent to the following one. Definition 1.4 (global convexity, geometrical point of view).…”

“…We recall that also the definition of causal convexity can be given, see, for example, [7] (see also [3]). …”

Geodesic connectedness of semi-Riemannian manifolds

“…6]). On the other hand, for the standard static case, a different variational principle in [44] solves completely the problem of connecting a point and a integral curve of ∂ t , for arbitrary M 0 (or D 0 ), [6].…”