Generalised time functions and finiteness of the Lorentzian distance

2014/12/17 by Rennie, Adam, Whale, Ben E. · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.1412.5652

Abstract

We show that finiteness of the Lorentzian distance is equivalent to the existence of generalised time functions with gradient uniformly bounded away from light cones. To derive this result we introduce new techniques to construct and manipulate achronal sets. As a consequence of these techniques we obtain a functional description of the Lorentzian distance extending the work of Franco and Moretti.

Cited by

• Limit curve theorems for incomplete metric spaces and the null distance on Lorentzian manifolds
• The representation of spacetime through time functions

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