# On null geodesically complete spacetimes uder NEC and NGC; is the Gao-Wald "time dilation" a topological effect?

## TL;DR

This paper reviews Gao-Wald's gravitational time delay theorem in null geodesically complete spacetimes, arguing it is topological rather than purely physical, especially when considering finer spacetime topologies.

## Contribution

It challenges the physical interpretation of Gao-Wald's theorem by highlighting its topological nature and explores implications for cosmological models without particle horizons.

## Key findings

- Gao-Wald theorem is not valid throughout its original statement.
- Certain cosmological models lack particle horizons when using finer topologies.
- Time dilation effects may be topological rather than physical phenomena.

## 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-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 "time dilation" theorems of this kind are topological in nature rather than having a particular physical meaning.