The representation of spacetime through steep time functions

@article{Minguzzi2018TheRO,
  title={The representation of spacetime through steep time functions},
  author={Ettore Minguzzi},
  journal={Journal of Physics: Conference Series},
  year={2018},
  volume={968}
}
  • E. Minguzzi
  • Published 31 October 2017
  • Mathematics
  • Journal of Physics: Conference Series
In a recent work I showed that the family of smooth steep time functions can be used to recover the order, the topology and the (Lorentz-Finsler) distance of spacetime. In this work I present the main ideas entering the proof of the (smooth) distance formula, particularly the product trick which converts metric statements into causal ones. The paper ends with a second proof of the distance formula valid for globally hyperbolic Lorentzian spacetimes. 
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