Geometric flows in Horava-Lifshitz gravity

TL;DR

This paper explores instanton solutions in four-dimensional Euclidean Horava-Lifshitz gravity, describing geometric flows driven by Cotton and Ricci tensors, analyzing fixed points, stability, and classifying solutions with SU(2) symmetry.

Contribution

It introduces a detailed analysis of geometric flows and instanton solutions in Horava-Lifshitz gravity, including stability and classification of fixed points with SU(2) symmetry.

Findings

Existence of finite-action instantons interpolating between fixed points.

Identification of stable and unstable fixed points in the flow.

Complete classification of solutions with SU(2) isometry.

Abstract

We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature terms can have competing behavior leading to a variety of fixed points. The instantons interpolate between any two fixed points, which are vacua of topologically massive gravity with Lambda > 0, and their action is finite. Special emphasis is placed on configurations with SU(2) isometry associated with homogeneous but generally non-isotropic Bianchi IX model geometries. In this case, the combined Ricci-Cotton flow reduces to an autonomous system of ordinary differential equations whose properties are studied in detail for different couplings. The occurrence and stability of isotropic and anisotropic fixed points are investigated analytically and some exact solutions are obtained. The corresponding instantons are classified and they are all globally R x S^3 and complete spaces. Generalizations to higher-dimensional gravities are also briefly discussed.