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Elsevier, Nonlinear Analysis: Theory, Methods and Applications, 5-7(63), p. e455-e463

DOI: 10.1016/j.na.2004.09.009

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On the Geometry of Static Spacetimes

Journal article published in 2004 by Miguel Sanchez ORCID
This paper is available in a repository.
This paper is available in a repository.

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