Causal and conformal structures of two-dimensional globally hyperbolic spacetimes

The group of conformal diffeomorphisms and the group of causal automorphisms on two-dimensional globally hyperbolic spacetimes are clarified. It is shown that if two-dimensional spacetimes have non-compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Minkowski spacetime, and if two-dimensional spacetimes have compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Einstein’s static universe. Also, the groups of such spacetimes are explicitly calculated by use of universal covering spaces.