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Global hyperbolicity and Palais-Smale condition for action functionals in stationary spacetimes

Anna Maria Candela·Jose' Luis Flores·Miguel Sanchez
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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.

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Anna Maria Candela, Jose' Luis Flores, Miguel Sanchez. 2006-10-05. Global hyperbolicity and Palais-Smale condition for action functionals in stationary spacetimes. https://arxiv.org/abs/math/0610175

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