The cosmological time function

Lars Andersson, Gregory J Galloway, Ralph Howard

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

Let (M, g) be a time-oriented Lorentzian manifold and d the Lorentzian distance on M. The function τ(q) := sup p<q d(p, q) is the cosmological time function of M, where as usual p < q means that p is in the causal past of q. This function is called regular iff τ(q) < ∞ for all q and also τ → 0 along every past inextendible causal curve. If the cosmological time function r of a spacetime (M, g) is regular it has several pleasant consequences: (i) it forces (M, g) to be globally hyperbolic; (ii) every point of (M, g) can be connected to the initial singularity by a rest curve (i.e. a timelike geodesic ray that maximizes the distance to the singularity); (iii) the function τ is a time function in the usual sense; in particular, (iv) τ is continuous, in fact, locally Lipschitz and the second derivatives of τ exist almost everywhere.

Original languageEnglish (US)
Pages (from-to)309-322
Number of pages14
JournalClassical and Quantum Gravity
Volume15
Issue number2
DOIs
StatePublished - Feb 1998

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time functions
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The cosmological time function. / Andersson, Lars; Galloway, Gregory J; Howard, Ralph.

In: Classical and Quantum Gravity, Vol. 15, No. 2, 02.1998, p. 309-322.

Research output: Contribution to journalArticle

Andersson, Lars ; Galloway, Gregory J ; Howard, Ralph. / The cosmological time function. In: Classical and Quantum Gravity. 1998 ; Vol. 15, No. 2. pp. 309-322.
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