Causal Isomorphism Between Globally Hyperbolic Spacetimes

In this paper, we show that every causal isomorphism between the causal future of the Cauchy surfaces of two globally hyperbolic spacetimes with non-compact Cauchy surface can be related to a unique order-isomorphism between its admissible systems. Conversely, we establish that every order-isomorphism between admissible systems can be related to a unique causal isomorphism between the causal future of its Cauchy surfaces.