Unimodular conformal and projective relativity
Physics Department, Boston University - Boston, MA 02215, USA
2 Center for Einstein Studies, Boston University - Boston, MA 02215, USA
Accepted: 15 November 2011
We outline unimodular conformal and projective relativity (UCPR), an extension of unimodular relativity in which the conformal and projective structures play central roles. Under symmetry group, the pseudo-Riemannian metric naturally decomposes into a four-volume element and a conformal metric; and the affine connection decomposes into a one-form and a trace-free projective connection. In UCPR, these four space-time structures are treated as independent fields that have clear physical interpretations. A Palatini-type variational principle for the usual general relativity Lagrangian leads to a breakup of the Einstein field equations and the compatibility conditions between the metric and connection. We indicate how new gravitational theories may be generated by modifications of this Lagrangian and discuss two such cases. Finally, we discuss possible physical consequences of our results for quantum gravity.
PACS: 04.20.-q – Classical general relativity / 04.20.Cv – Fundamental problems and general formalism / 02.40.-k – Geometry, differential geometry, and topology
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