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Stable causality, lightlike lines and time functions in General Relativity
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The causal ladder of spacetimes is introduced and the role
of stable causality is commented. Some details are given of the recent
solution to the problem of the equivalence between stable causality
and K-causality. In particular this result is used to show that under
reasonable conditions the absence of a cosmological time implies the
null geodesic singularity of spacetime. It is also shown that the time
functions are utilities for the K (Seifert) relation, the concept of
utility being originally introduced in microeconomics. This approach
allows us to use result imported from microeconomics to prove that the
K relation can be recovered from the set of time or temporal functions.
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