Anti-de Sitter gauge theory for gravity

Abstract

First a review is given of Riemann-Cartan space-time and Einstein-Cartan gravity. This gives us the necessary tools to handle the SO(2,3) Yang-Mills gauge theory for gravity. Field equations are obtained from a Yang-Mills gauge field Lagrangian. From these field equations and the Bianchi identities the conservation laws for anti-de Sitter theory are derived. Possible solutions of the field equations are discussed. The only solution found for a RW-geometry with a perfect fluid matter content is the early universe. There are no Schwarzschild solutions of the torsion free vacuum field equations if curvature squared terms cannot be neglected.

arXiv comment39 pages; In section 5.2 more detail is given in the calculation of the field equations. Section 6 (Discussion) has been added. Table of contents added. References extended and links added. Remarks Euler-form added