On the alternative description of complex holomorphic and Lorentz geometries in four dimensions
Abstract
The equivalence of a conformal metric on 4dimensional spacetime and a local field of 3dimensional subspaces of the space of 2forms over spacetime is discussed and the basic notion of transection is introduced. Corresponding relation is spread to the metric case in terms of notion of normalized ordered oriented transection field. As a result, one obtains a possibility to handle the metric geometry without any references to the metric tensor itself on a distinct base which nevertheless contains all the information on metricity. Moreover, the notion of spacetime curvature is provided with its natural counterpart in the transection `language' in a form of curvature endomorphism as well. To globalize the local constructions introduced, a certain fiber bundle is defined whose sections are equivalent to normalized ordered oriented transection fields and locally to the metric tensor on spacetime. The criterion distinguishing the Lorentz geometry is discussed. The resulting alternative method of the description of spacetime metricity, dealing with exterior forms foliation alone, seems to be of a power compatible with one of the standard concept based on the metric tensor.
 Publication:

arXiv eprints
 Pub Date:
 December 1993
 arXiv:
 arXiv:grqc/9312038
 Bibcode:
 1993gr.qc....12038T
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 29 pages, uuencoded compressed PostScript, no local #