Causal functions in general relativity. II
The author continues his joint work with \textit{U. D. Vyas} [ibid. 15, 553- 565 (1983; Zbl 0521.53052)] where different types of causality conditions for spacetimes had been described in terms of so-called causal functions. Several mathematical insufficiencies of this work had been detected by \textit{J. Dieckmann} who provided a corrected version of these causal functions in his thesis [Volumenfunktionen in der Allgemeinen Relativitätstheorie, Dissertation, TU Berlin (1987; Zbl 0612.53038)], containing an extended catalogue of such characterizations [see also Gen. Relativ. Gravitation 20, No.9, 859-867 (1988; Zbl 0645.53035)]. The main purpose of this note is to give a clarification of the author's earlier definition of a causal function and to characterize the conditions of stable causality and strong causality in terms of these functions. The characterizations given here are different from those which already have been obtained by Dieckmann (loc. cit.). Reviewer's remarks: The author quotes Dieckmann's criticism in a very improper way declaring Dieckmann's counterexample as unphysical. He sticks to consider the 'natural Euclidean measure' on the power set of \({\mathbb{R}}^ 4\) for example. The term of a causal function does not receive a precise mathematical definition in this article. This cannot be replaced by the argument of writing on some physical subjects only. Some particular example due to Dieckmann which is quoted as a private communication only can be found explicitly in the same journal (loc.cit.). Dieckmann's work is not mentioned in the references.
scientific article; zbMATH DE number 4190639