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

TL;DR

This paper explores symmetries in generalized gravitational actions, deriving field equations for higher-derivative theories, and discusses solutions and implications for the cosmological constant problem in string-inspired gravity models.

Contribution

It introduces new symmetry considerations in higher-derivative gravity theories and analyzes their solutions within the first-order formalism, extending understanding of string effective actions.

Findings

Existence of particular solutions satisfying vacuum equations with cosmological constant.

Derivation of field equations for various higher-derivative theories.

Implications for the cosmological constant problem from generalized symmetries.

Abstract

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.