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Poincaré gauge theory of gravitation: Foundations, exact solutions and computer algebra

  • J. Dermott Mc Crea
III. Classical And Quantized Field Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1251)

Abstract

A framework is developed for the gauge theory of the Poincaré (or inhomogeneous Lorentz) group. A first-order Lagrangian formalism is set up in a Riemann-Cartan space-time, which will be characterized by means of an orthonormal tetrad basis and and a metric-compatible connection. The sources of gravity are mass and spin. The basis 1-forms and the connection 1-forms turn out to be the gravitational potentials, both obeying a field equation of at most second order in the derivatives. Gravitational energy-momentum and spin currents are derived and a class of Lagrangians of the Poincaré gauge fields specified, which is polynomial in the torsion and the curvature up to the second order. This yields quasilinear gravitational field equations. Exact solutions for a specific choice of Lagrangian are discussed, as well as the application of the symbolic computing system, REDUCE, in the derivation of these solutions.

Keywords

Gauge Theory Field Equation Gauge Field Vacuum Solution Spin Current 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. Dermott Mc Crea
    • 1
  1. 1.Department of Mathematical PhysicsUniversity CollegeDublin 4Ireland

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