Static space–times naturally lead to quasi-pseudometrics

Authors:
Hans-Peter A. Künzi;Vladik Kreinovich
Affiliations:
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa;Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

The standard 4-dimensional Minkowski space-time of special relativity is based on the 3-dimensional Euclidean metric. In 1967, H. Busemann showed that similar static space-time models can be based on an arbitrary metric space. In this paper, we search for the broadest possible generalization of a metric under which a construction of a static space-time leads to a physically reasonable space-time model. It turns out that this broadest possible generalization is related to the known notion of a quasi-pseudometric.