On null geodesically complete spacetimes under NEC and NGC: Is the Gao‐Wald “time dilation” a topological effect?

Abstract

We review a theorem of Gao‐Wald on a kind of a gravitational “time delay” effect in null geodesically complete spacetimes under NEC and NGC, and we observe that it is not valid anymore throughout its statement, as well as a conclusion that there is a class of cosmological models where particle horizons are absent, if one substituted the manifold topology with a finer (spacetime) topology. Since topologies of the Zeeman‐Göbel 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 “time dilation” theorems of this kind are topological in nature rather than having a particular physical meaning.