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

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 grav...

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Bibliographic Details
Main Author: Mc Crea, J. Dermott
Format: Book Chapter
Language:English
Subjects:
Field Equation
Gauge Field
Gauge Theory
Spin Current
Vacuum Solution
Online Access:Get full text
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Summary: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.
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0077323