Linking Past and Future Null Infinity in Three Dimensions

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.
Comment: 7 pages, 3 figures; added references and appendix, matches published version