On null geodesically complete spacetimes uder NEC and NGC; is time dilation a topological effect?

We review a theorem of Gao-Wald on gravitational time delay in null geodesically complete spacetimes under NEC and NGC, and we observe that it is not valid anymore throuhout its statement, if one substituted the manifold topology with a finer (spacetime-) topology. Since topologies of the Zeeman-G\"obel class incorporate the causal, differential and conformal structure of a spacetime, and there are serious mathematical arguments in favour of such topologies and against the manifold topology, there is a strong evidence that such time dilation theorems are not ``natural'' but are an effect of the use of an ``artificial'' topology (like the manifold one).