  We prove that any simply-connected globally hyperbolic conformally flat
spacetime V can be conformally embedded in a bigger conformally flat spacetime,
called enveloping space of V , containing all the conformally flat
Cauchy-extensions of V , in particular its C 0-maximal extension. As a result,
we establish a new proof of the existence and the uniqueness of the C 0-maximal
extension of a globally hyperbolic conformally flat spacetime. Furthermore,
this approach allows us to prove that C 0-maximal extensions respect inclusion.
