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Time And Dark Matter From The Conformal Symmetries Of Euclidean Space, Jeffrey S. Hazboun, James Thomas Wheeler
Time And Dark Matter From The Conformal Symmetries Of Euclidean Space, Jeffrey S. Hazboun, James Thomas Wheeler
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The quotient of the conformal group of Euclidean 4-space by its Weyl subgroup results in a geometry possessing many of the properties of relativistic phase space, including both a natural symplectic form and non-degenerate Killing metric. We show that the general solution posesses orthogonal Lagrangian submanifolds, with the induced metric and the spin connection on the submanifolds necessarily Lorentzian, despite the Euclidean starting pont. By examining the structure equations of the biconformal space in an orthonormal frame adapted to its phase space properties, we also find that two new tensor fields exist in this geometry, not present in Riemannian geometry. …
Weyl Gravity As General Relativity, James Thomas Wheeler
Weyl Gravity As General Relativity, James Thomas Wheeler
James Thomas Wheeler
When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This result differs strongly from the usual fourth-order formulation of Weyl gravity.