Year: 1998
Type: article
Abstract: 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.
Source: Classical and Quantum Gravity
Authors: Lars Andersson, Gregory J Galloway, Ralph Howard
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1982662190