GAUGE-INVARIANT VARIABLES IN GENERAL RELATIVITY
Abstract
Einstein's field equations for the gravitational field possess solutions having a large variety of topological properties; among them there are solutions whose curvature goes asymptotically to zero at spatial infinity. If we restrict our elves to s lutions that are asymptotically Minkowskian, then it is tempting to try to divide the effects of curvilinear coordinate transformations into th se that correspond to a Lorentz transformation and those that represent gaugetype effects. The group-theoretical aspects of such schemes are analyzed. Making a definiteASSUMPTION CONCERNING THE GROUP OF CURVILINEAR TRANSFORMATIONS THAT WILL PRESERVE THE ASYMPTOTIC Minkowski character of the metric field, it is concluded that t e reduction to a Lorentz-covariant theory is in fact impossible. The course of the analysis suggests, ho ever, that this negative result depends on the initial group of transformations adopted; it is conceivable that a slightly different invariance group would be compatible with a special-relativistic formulation of the heory. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1961
- Accession Number
- AD0261030
Entities
People
- Peter G. Bergmann
Organizations
- Syracuse University