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arXiv · gr-qc/9910039

Quadratic Lagrangians and Topology in Gauge Theory Gravity

Antony Lewis·Chris Doran·Anthony Lasenby
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Abstract

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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Antony Lewis, Chris Doran, Anthony Lasenby. 1999-10-12. Quadratic Lagrangians and Topology in Gauge Theory Gravity. https://doi.org/10.1023/a%3A1001856702156

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