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The cosmological time function

MPG-Autoren
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Andersson,  Lars
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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cosmological-1.pdf
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Zitation

Andersson, L., Galloway, G. J., & Howard, R. (1998). The cosmological time function. Classical and Quantum Gravity, 15(2), 309-322.


Zitierlink: https://hdl.handle.net/11858/00-001M-0000-0013-596E-0
Zusammenfassung
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.