A certain space-time metric and smooth general connections
type: Item
instance of: scholarly article
title: A certain space-time metric and smooth general connections
zbMATH Open document ID: 0589.53015
author: Tominosuke Otsuki
published in: Kodai Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: The notion of general connection was introduced by the author [Math. J. Okayama Univ. 9, 99-164 (1960; Zbl 0202.211)]. Recently he gave a construction of a space with general connections, which has points swallowing geodesics [ibid. 24, 157-165 (1982; Zbl 0502.53050)]. A set which swallows geodesics is called a black hole. In this paper the space-time metric \[ (*)\quad d\sigma^ 2=-(1-4m^ 2/r^ 2)dt^ 2+(2/r)dt dr+r^ 2(d\theta^ 2+\sin^ 2\theta d^ 2\phi) \] is considered. It is shown that this metric has the curve \(r=0\) in \(R\times R^ 3\) as a black hole for the system of visible geodesics. Then a general connection is found which is smooth on \(R\times R^ 3\) and has the same system of geodesics as the one of the metric (*).
Mathematics Subject Classification ID: 53B15
Mathematics Subject Classification ID: 53B50
zbMATH DE Number: 3947082
zbMATH Keywords: Eddington-Finkelstein metric
zbMATH Keywords: general connection
zbMATH Keywords: black hole
reviewed by: Mihai Anastasiei
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037098
OpenAlex ID: W2051438202
cites work: Q5596028
cites work: Q5599509
cites work: Q3277862
cites work: On metric general connections
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cites work: General connections $A\Gamma A$ amd the parallelism of Levi-Civita
cites work: Q3968114
DOI: 10.2996/KMJ/1138037098
description: scientific article; zbMATH DE number 3947082