2010/02/28 by Ioannis Bakas, Francois Bourliot, François Bourliot +3 · 2 citations
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Curvature #Diffeomorphism #Differential geometry #Euclidean geometry #Fixed point #Flow (mathematics) #Instanton #Isometry (Riemannian geometry) #Isotropy #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1007/jhep04(2010)131
67 pages, 16 figures; more solutions found, 1 extra figure, 1 more reference added in v2; minor typos corrected in v3 (to appear in JHEP); an acknowledgement added in v4
openalex publication_date 2010/04/01 · arxiv created 2011/04/07 · arxiv updated 2015/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider instanton solutions of Euclidean Hořava-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 Λ > 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 × S3 and complete spaces. Generalizations to higher-dimensional gravities are also briey discussed.