On the conformal group of a globally hyperbolic spacetime

The Groups of causal and conformal automorphisms of globally hyperbolic spacetimes were studied. In two dimensions, we prove that all globally hyperbolic spacetimes that are directed and connected are causally isomorphic. We work out the consequences of this fact and obtain a (partial) classification of the causal automorphism and conformal groups of a two-dimensional globally hyperbolic space. Finally, we present a generalization for locally conformally flat globally hyperbolic spacetimes.