On the metric structure of space-time

Details On the metric structure of space-time On the metric structure of space-time

2010-09-28

arxiv.org/abs/1009.5523v1

M. A. del Olmo, M. Santander, and J. Mateos Guilarte, eds., Group Theoretical Methods in Physics, Vol. II, Anales de Fisica, M

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

I present an analysis of the physical assumptions needed to obtain the metric structure of space-time. For this purpose I combine the axiomatic approach pioneered by Robb with ideas drawn from works on Weyl's "Raumproblem". The concept of a Lorentzian manifold is replaced by the weaker concept of an "event manifold", defined in terms of volume element, causal structure and affine connection(s). Exploiting properties of its structure group, I show that distinguishing Lorentzian manifolds from other classes of event manifolds requires the key idea of general relativity: namely that the manifold's physical structure, rather than being fixed, is itself a variable.

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