Global hyperbolicity and Palais-Smale condition for action functionals in stationary spacetimes
Differential Geometry
2013-04-18 v1 General Relativity and Quantum Cosmology
Abstract
In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients of the metric, etc. We prove that these technical assumptions admit a natural interpretation for the conformal structure (causality) of the manifold. As a consequence, any stationary spacetime with a complete timelike Killing vector field and a complete Cauchy hypersurface (thus, globally hyperbolic), is proved to be geodesically connected.
Cite
@article{arxiv.math/0610175,
title = {Global hyperbolicity and Palais-Smale condition for action functionals in stationary spacetimes},
author = {Anna Maria Candela and Jose' Luis Flores and Miguel Sanchez},
journal= {arXiv preprint arXiv:math/0610175},
year = {2013}
}