Metric completeness of C(p, q) in a globally hyperbolic spacetime

Autor:	H. S. Mondal, Binayak S. Choudhury
Rok vydání:	2014
Předmět:	Physics Causality (physics) Sequence Pure mathematics Cauchy surface Spacetime Completeness (order theory) Metric (mathematics) Astronomy and Astrophysics Cauchy sequence Complete metric space
Zdroj:	Gravitation and Cosmology. 20:144-147
ISSN:	1995-0721 0202-2893
Popis:	We consider a Lorentzian manifold M which is globally hyperbolic. We define a metric on C(p, q), the set of all equivalence classes of causal curves connecting two causally related points p and q. We show that C(p, q) is a complete metric space with the metric thus defined. Here, by completeness we mean that every Cauchy sequence (a sequence with a tendency to converge) in C(p, q) finds a point in it to converge. We also give an example to show that the result does not hold in general when the spacetime is not globally hyperbolic. The work is in line with research on causality in relativistic spacetimes.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::36af3aec5c324cfc2943c2d21c9f45ef https://doi.org/10.1134/s0202289314020029 Zobrazit plný text záznamu Full text from SpringerLink