Static space–times naturally lead to quasi-pseudometrics

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.