Lars Andersson et al 1998 Class. Quantum Grav. 15 309 doi:10.1088/0264-9381/15/2/006
The cosmological time function
Lars Andersson
, Gregory J Galloway
and Ralph Howard§
Let 
be a time-oriented Lorentzian manifold and d the Lorentzian distance on M. The function 
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 
for all q and also 
along every past inextendible causal curve. If the cosmological time function 
of a spacetime is regular it has several pleasant consequences: (i) it forces to be globally hyperbolic; (ii) every point of 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 is a time function in the usual sense; in particular, (iv) is continuous, in fact, locally Lipschitz and the second derivatives of exist almost everywhere.
- PACS
-
02.40.-k Geometry, differential geometry, and topology
04.20.Gz Spacetime topology, causal structure, spinor structure
- MSC
-
53C50 Lorentz manifolds, manifolds with indefinite metrics
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
- Subjects
- Dates
-
Issue 2 (February 1998)
Received 29 July 1997
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The cosmological time function
Lars Andersson et al 1998 Class. Quantum Grav. 15 309
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