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On null geodesically complete spacetimes under NEC and NGC: is the Gao-Wald “time dilation” a topological effect? (English) Zbl 1445.83002

Summary: 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 [R. Göbel, Commun. Math. Phys. 46, 289–307 (1976; Zbl 0324.57002)] 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.

MSC:

83C10 Equations of motion in general relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C40 Gravitational energy and conservation laws; groups of motions
83F05 Relativistic cosmology
54F65 Topological characterizations of particular spaces
57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
53Z05 Applications of differential geometry to physics

Citations:

Zbl 0324.57002

References:

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