Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-06-25
Phys.Rev.D81:104001,2010
Physics
High Energy Physics
High Energy Physics - Theory
14 pages
Scientific paper
10.1103/PhysRevD.81.104001
We discuss four-dimensional "spatially homogeneous" gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein's equations with potentially non-vanishing cosmological constant. They are endowed with a product structure R \times M_3 leading to a natural foliation into three-dimensional subspaces evolving in Euclidean time. For a large class of three-dimensional subspaces, the dynamics coincides with the geometric flow on the three-dimensional homogeneous slice, driven by the Ricci tensor plus an so(3) gauge connection. The metric on the three-dimensional space is related to the vielbein of the three-dimensional subspace, while the gauge field is inherited from the anti-self-dual component of the four-dimensional Levi--Civita connection.
Bourliot Francois
Estes John
Petropoulos Marios. P.
Spindel Ph
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