Causal functions in general relativity. II
type: Item
instance of: scholarly article
title: Causal functions in general relativity. II
zbMATH Open document ID: 0722.53060
DOI: 10.1007/BF00763310
published in: General Relativity and Gravitation
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83C75
zbMATH DE Number: 4190639
zbMATH Keywords: causality conditions
zbMATH Keywords: causal functions
zbMATH Keywords: stable causality
zbMATH Keywords: strong causality
author: Pankaj S. Joshi
reviewed by: Bernd Wegner
MaRDI profile type: Publication
cites work: Causal functions in General Relativity
cites work: The Large Scale Structure of Space-Time
cites work: Domain of Dependence
cites work: The causal boundary of space-times
cites work: Q4084319
cites work: Distinguishing properties of causality conditions
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description: scientific article; zbMATH DE number 4190639