On the Geometry of Static Spacetimes

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 $\beta$, ${\beta }^{-1}$ ($\beta =-g(K,K)$, being $K$ a timelike irrotational Killing vector field), which essentially control completeness, causality and geodesic connectedness. Recent references are specially discussed.

Minor changes, 12 pages, refereed contribution for the 4th World Congress of Nonlinear Analysts, Orlando (Florida), June 30-July 7 (2004)

Cited by in corpus (1)

• Klein-Gordon Solutions on Non-Globally Hyperbolic Standard Static Spacetimes