TY - JOUR

T1 - The cosmological time function

AU - Andersson, Lars

AU - Galloway, Gregory J.

AU - Howard, Ralph

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 1998/2

Y1 - 1998/2

N2 - Let (M, g) be a time-oriented Lorentzian manifold and d the Lorentzian distance on M. The function τ(q) := supp 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.

AB - Let (M, g) be a time-oriented Lorentzian manifold and d the Lorentzian distance on M. The function τ(q) := supp 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.

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U2 - 10.1088/0264-9381/15/2/006

DO - 10.1088/0264-9381/15/2/006

M3 - Article

AN - SCOPUS:0032340442

VL - 15

SP - 309

EP - 322

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 2

ER -