Quadratic Lagrangians and Topology in Gauge Theory Gravity

Details Quadratic Lagrangians and Topology in Gauge Theory Gravity Quadratic Lagrangians and Topology in Gauge Theory Gravity

1999-10-12

arxiv.org/abs/gr-qc/9910039v1

Gen.Rel.Grav. 32 (2000) 161-173

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

We consider topological contributions to the action integral in a gauge theory formulation of gravity. Two topological invariants are found and are shown to arise from the scalar and pseudoscalar parts of a single integral. Neither of these action integrals contribute to the classical field equations. An identity is found for the invariants that is valid for non-symmetric Riemann tensors, generalizing the usual GR expression for the topological invariants. The link with Yang-Mills instantons in Euclidean gravity is also explored. Ten independent quadratic terms are constructed from the Riemann tensor, and the topological invariants reduce these to eight possible independent terms for a quadratic Lagrangian. The resulting field equations for the parity non-violating terms are presented. Our derivations of these results are considerably simpler that those found in the literature.

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