Recent Developments in Pseudo-Riemannian Geometry


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pp: 299–358

DOI: 10.4171/051-1/9

The causal hierarchy of spacetimes

Ettore Minguzzi[1] and Miguel Sánchez[2]

(1) Dipartimento di Matematica Applicata, Universita di Firenze, Via S. Marta 3, 50139, FIRENZE, ITALY
(2) Departamento de Geometría y Topología, Universidad de Granada, Avda Fuentenueva s/n, 18071, GRANADA, SPAIN

The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved “folk questions on smoothability”, and alternative proposals (as recent isocausality), are also summarized.

Keywords: Lorentzian geometry, spacetime, conformal invariance, ladder of causality, Cauchy hypersurface, causal geodesic, static spacetime, closed timelike geodesic, conjugate points on lightlike pregeodesics, continuous causal curve

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