Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-11-01
Int.J.Geom.Methods Mod.Phys.08 2011:273-301,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
21 pages (Reduced to clarify and focus on central argument; some calculations condensed; typos corrected)
Scientific paper
10.1142/S0219887811005130
Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a derived property of general relativity.
Spencer Joseph Andrew
Wheeler James T.
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