759 research outputs found
Ricci flow of unwarped and warped product manifolds
We analyse Ricci flow (normalised/un-normalised) of product manifolds
--unwarped as well as warped, through a study of generic examples. First, we
investigate such flows for the unwarped scenario with manifolds of the type
, , and also, similar multiple products. We are able to
single out generic features such as singularity formation, isotropisation at
particular values of the flow parameter and evolution characteristics.
Subsequently, motivated by warped braneworlds and extra dimensions, we look at
Ricci flows of warped spacetimes. Here, we are able to find analytic solutions
for a special case by variable separation. For others we numerically solve the
equations (for both the forward and backward flow) and draw certain useful
inferences about the evolution of the warp factor, the scalar curvature as well
the occurence of singularities at finite values of the flow parameter. We also
investigate the dependence of the singularities of the flow on the inital
conditions. We expect our results to be useful in any physical/mathematical
context where such product manifolds may arise.Comment: 25 pages, 25 figures, some figures replace
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