Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity

Details Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity

1996-08-10

arxiv.org/abs/gr-qc/9608025v3

Gen.Rel.Grav. 30 (1998) 345-377

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pages, TeX. Additional remarks concerning the gravitational action are included in section 4

Scientific paper

Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the first-order formalism are derived, and variations of a generic set of higher-order curvature terms appearing in string effective actions are studied. It is shown that there often exists a particular set of solutions to the field equations of pure gravity theories, consisting of different combinations of curvature tensors, which satisfies the vacuum equations with cosmological constant. Implications of generalized symmetries of the field equations derived from the superstring effective action for the cosmological constant problem are discussed.

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