Reachable sets for a class of contact sub-lorentzian metrics on $\mathbb{R}^{3}$, and null non-smooth geodesics
Volume 82 / 2008
Banach Center Publications 82 (2008), 101-110
MSC: 53C50.
DOI: 10.4064/bc82-0-7
Abstract
We compute future timelike and nonspacelike reachable sets from the origin for a class of contact sub-Lorentzian metrics on $\mathbb{R}% ^{3}$. Then we construct non-smooth (and therefore non-Hamiltonian) null geodesics for these metrics. As a consequence we deduce that the sub-Lorentzian distance from the origin is continuous at points belonging to the boundary of the reachable set.
