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

Tags

DTIC Thesaurus Topics

  • Curvature
  • Differential Equations
  • Equations
  • General Relativity
  • Geometric Forms
  • Geometry
  • Gravitational Fields
  • Invariance
  • Lines (Geometry)
  • Mathematics
  • Partial Differential Equations
  • Personality

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.
  • Plasma Physics / Magnetohydrodynamics