A ug 2 00 8 Ricci Solitons and Einstein - Scalar Field Theory
نویسندگان
چکیده
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.
منابع مشابه
On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons
The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...
متن کاملJa n 20 09 Ricci Solitons and Einstein - Scalar Field Theory
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...
متن کاملEinstein structures on four-dimensional nutral Lie groups
When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...
متن کاملدستهای از جوابهای دقیق گرانش با مشتقات بالاتر در چهار بعد
In this paper we consider the action of higher derivative gravity up to the second order terms in the scalars made from the Ricci scalar, Ricci and Riemann tensors. We use the Bach- Lanczos identity of the Weyl tensor in four dimensions and show that the solutions of 4-dimensional Einstein equations with cosmological constant term in vacuum, which are known as Einstein metrics, satisfy the fie...
متن کاملWarped product and quasi-Einstein metrics
Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کامل