With the development of optimal transportation in Riemannian geometry and its connections to mathematical physics it is natural to look for an analogue in Lorentzian geometry. I will give a motivation for the Lorentzian cost function and shortly discuss first results in Lorentzian optimal transport.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/7138