All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Classical and Quantum Gravity

Volume

19

Issue

4

Publisher

Institute of Physics

Publication Date

2002

First Page

641

Last Page

675

DOI

10.1088/0264-9381/19/4/303

Abstract

We consider a version of Palais' principle of symmetric criticality (PSC) that is applicable to the Lie symmetry reduction of Lagrangian field theories. Given a group action on a space of fields, PSC asserts that for any group-invariant Lagrangian, the equations obtained by restriction of Euler–Lagrange equations to group-invariant fields are equivalent to the Euler–Lagrange equations of a canonically defined, symmetry-reduced Lagrangian. We investigate the validity of PSC for local gravitational theories built from a metric and show that there are two independent conditions which must be satisfied for PSC to be valid. One of these conditions, obtained previously in the context of transverse symmetry group actions, provides a generalization of the well-known unimodularity condition that arises in spatially homogeneous cosmological models. The other condition seems to be new. These results are illustrated with a variety of examples from general relativity.

Comments

Originally published by the Institute of Physics. Publisher's PDF can be accessed through Classical and Quantum Gravity. Article is also available online through arXiv.org.

http://arxiv.org/abs/gr-qc/0108033