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 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.