On the Geometry of Static Spacetimes

Details On the Geometry of Static Spacetimes On the Geometry of Static Spacetimes

2004-06-16

arxiv.org/abs/math/0406332v2

Nonlinear Analysis 63 (2005) e455-e463

Mathematics

Differential Geometry

Minor changes, 12 pages, refereed contribution for the 4th World Congress of Nonlinear Analysts, Orlando (Florida), June 30-Ju

Scientific paper

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 $\beta$, $\beta^{-1}$ ($\beta = -g(K,K)$, 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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