Self-dual gravitational instantons and geometric flows of all Bianchi types

Abstract

We investigate four-dimensional, self-dual gravitational instantons endowed with a product structure RxM_3, where M_3 is homogeneous of Bianchi type. We analyze the general conditions under which Euclidean-time evolution in the gravitational instanton can be identified with a geometric flow of a metric on M_3. This includes both unimodular and non-unimodular groups, and the corresponding geometric flow is a general Ricci plus Yang-Mills flow accompanied by a diffeomorphism.

Latex, 12 pages; Final version

References in corpus (5)

• Membranes at Quantum Criticality
• Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary
• Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem
• Gravitational instantons, self-duality and geometric flows
• G3-homogeneous gravitational instantons

Cited by in corpus (3)

• Gravitational duality, topologically massive gravity and holographic fluids
• Soliton metrics for two-loop renormalization group flow on 3D unimodular Lie groups
• Higher order geometric flows on three dimensional locally homogeneous spaces