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On the Geometry of Static Spacetimes

Miguel Sanchez
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Abstract

We review geometrical properties of a static spacetime $(M,g)$, including geodesic completeness, causality, standard splittings, compact $M$, closed geodesics and geodesic connectedness. We pay special attention to the critical quadratic behavior at infinity of the coefficients $β$, $β^{-1}$ ($β= -g(K,K)$, being $K$ a timelike irrotational Killing vector field), which essentially control completeness, causality and geodesic connectedness. Recent references are specially discussed.

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Miguel Sanchez. 2004-06-26. On the Geometry of Static Spacetimes. https://arxiv.org/abs/math/0406332

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