How to detect the spacetime curvature without rulers and clocks

A. V. Nenashev; S. D. Baranovskii

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arXiv · 2302.12209

How to detect the spacetime curvature without rulers and clocks

A. V. Nenashev·S. D. Baranovskii

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Abstract

We demonstrate how one can distinguish a curved 4-dimensional spacetime from a flat one, when it is possible, relying only on the causality relations between events. It is known that it is possible only for spacetimes that are not conformally flat. We prove that if a spacetime is not conformally flat, then its non-flatness can be verified by only a few (sixteen) measurements of causal relations. Therefore the results of this paper clarify what can be said about flatness or non-flatness of the spacetime after a finite number of measurements of causal relations.

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A. V. Nenashev, S. D. Baranovskii. 2023-02-23. How to detect the spacetime curvature without rulers and clocks. https://arxiv.org/abs/2302.12209

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