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 Mat. Tr., 2014, Volume 17, Number 2, Pages 41–60 (Mi mt276)

Functions with (non)timelike gradient on a space-time

V. N. Berestovskiĭ, I. A. Zubareva

Sobolev Institute of Mathematics, Omsk Division, Omsk, 644099, Russia

Abstract: We consider some generalization of a problem proposed by V. A. Toponogov for functions with nontimelike gradient on a globally hyperbolic space-time and a specific application of the positive solution of this problem to the cases of a Minkowski space-time and a de Sitter space-time of the first kind. Examples of smooth functions with timelike gradient on Lorentz manifolds are given. The authors obtain some sufficient conditions for level surfaces of functions with timelike gradient on a Lorentz manifold which guarantee that the manifold is globally hyperbolic. A description of the past and the future event horizons for timelike geodesics in a de Sitter space-time of the first kind is given. Some unsolved problems are formulated.

Key words: globally hyperbolic space-time, Cauchy surface, (non)timelike gradient, Lorentz manifold, level surface, de Sitter space-time of the first kind, world line, event horizon.

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English version:
Siberian Advances in Mathematics, 2015, 25:4, 243–254

Bibliographic databases:

Document Type: Article
UDC: 517.1+514.76

Citation: V. N. Berestovskiǐ, I. A. Zubareva, “Functions with (non)timelike gradient on a space-time”, Mat. Tr., 17:2 (2014), 41–60; Siberian Adv. Math., 25:4 (2015), 243–254

Citation in format AMSBIB
\Bibitem{BerZub14} \by V.~N.~Berestovski{\v\i}, I.~A.~Zubareva \paper Functions with (non)timelike gradient on a~space-time \jour Mat. Tr. \yr 2014 \vol 17 \issue 2 \pages 41--60 \mathnet{http://mi.mathnet.ru/mt276} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3330050} \transl \jour Siberian Adv. Math. \yr 2015 \vol 25 \issue 4 \pages 243--254 \crossref{https://doi.org/10.3103/S1055134415040021}