Unimodular conformal and projective relativity

Details Unimodular conformal and projective relativity Unimodular conformal and projective relativity

2011-10-10

arxiv.org/abs/1110.2159v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages. To appear in EPL. Abstract shortened. Equation typos fixed. Two references added since v1

Scientific paper

We outline unimodular conformal and projective relativity (UCPR), an extension of unimodular relativity in which the conformal and projective structures play central roles. Under $SL(4,\mathbb{R})$ 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.

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