Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-08-22
Class.Quant.Grav.26:055015,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages, 1 figure; Revised version (organizational changes, other minor revisions and corrections, citations corrected and ad
Scientific paper
10.1088/0264-9381/26/5/055015
B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a free massless scalar field with nonzero cosmological constant are associated to shrinking or expanding Ricci solitons. We exhibit examples, including an explicit family of complete expanding solitons which can be thought of as a Ricci flow for a complete Lorentzian metric. The possible generalization to Ricci-flat stationary metrics leads us to consider an alternative to Ricci flow.
Akbar M. M.
Woolgar Eric
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