1997/06/29 by James Thomas Wheeler, James T. Wheeler, Wheeler, James T.
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9706215
32 pages, plain TeX, no figures
arxiv created 1997/06/29 · openalex publication_date 1997/06/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new 8-dimensional conformal gauging avoids the unphysical size change, third order gravitational field equations, and auxiliary fields that prevent taking the conformal group as a fundamental symmetry. We give the structure equations, gauge transformations and intrinsic metric structure for the new biconformal spaces. We prove that a torsion-free biconformal space with exact Weyl form, closed dilational curvature and trace-free spacetime curvature admits a sub-bundle of vanishing Weyl form homeomorphic to the Whitney sum bundle of the tangent bundle and the bundle of orthonormal Lorentz frames over 4-dimensional spacetime. Conversely, any 4-dimensional spacetime extends uniquely to such a normal biconformal space. The Einstein equation holds if and only if the biconformal basis is orthonormal. Unconstrained antisymmetric trace of the spacetime curvature provides a closed 2-form, independent of the Weyl vector, consistently interpretable as the electromagnetic field. The trace of the spacetime co-torsion decouples from gravitational sources and serves as electromagnetic source.