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We compute future timelike and nonspacelike reachable sets from the origin for a class of contact sub-Lorentzian metrics on R. Then we construct non-smooth (and therefore non-Hamiltonian) null geodesics for these metrics. As a consequence we deduce that the subLorentzian distance from the origin is continuous at points belonging to the boundary of the reachable set.

Reachable sets for a class of contact sub-lorentzian metrics on R3, and null non-smooth geodesics

Reachable sets for a class of contact sub-lorentzian metrics on R³, and null non-smooth geodesics