Unimodular conformal and projective relativity
arXiv:1110.2159 · doi:10.1209/0295-5075/97/10001
Abstract
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.
6 pages. To appear in EPL. Abstract shortened. Equation typos fixed. Two references added since v1
References in corpus (10)
- Scale invariance, unimodular gravity and dark energy
- The quantization of unimodular gravity and the cosmological constant problem
- "No Information Without Disturbance": Quantum Limitations of Measurement
- On geodesic mappings of manifolds with affine connection
- Unimodular loop quantum gravity and the problems of time
- Unimodular cosmology and the weight of energy
- Instantons and unitarity in quantum cosmology with fixed four-volume
- Unimodular Loop Quantum Cosmology
- The symplectic 2-form and Poisson bracket of null canonical gravity
- Weyl Geometries and Timelike Geodesics