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More on Cotton flow
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Date
2015-06-22
Author
Kilicarslan, Ercan
Dengiz, Suat
Tekin, Bayram
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Cotton flow tends to evolve a given initial metric on a three manifold to a conformally flat one. Here we expound upon the earlier work on Cotton flow and study the linearized version of it around a generic initial metric by employing a modified form of the DeTurck trick. We show that the flow around the flat space, as a critical point, reduces to an anisotropic generalization of linearized KdV equation with complex dispersion relations one of which is an unstable mode, rendering the flat space unstable under small perturbations. We also show that Einstein spaces and some conformally flat non-Einstein spaces are linearly unstable. We refine the gradient flow formalism and compute the second variation of the entropy and show that generic critical points are extended Cotton solitons. We study some properties of these solutions and find a Topologically Massive soliton that is built from Cotton and Ricci solitons. In the Lorentzian signature, we also show that the pp-wave metrics are both Cotton and Ricci solitons.
Subject Keywords
Models of quantum gravity
,
Classical theories of gravity
URI
https://hdl.handle.net/11511/35564
Journal
JOURNAL OF HIGH ENERGY PHYSICS
DOI
https://doi.org/10.1007/jhep06(2015)136
Collections
Department of Physics, Article
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E. Kilicarslan, S. Dengiz, and B. Tekin, “More on Cotton flow,”
JOURNAL OF HIGH ENERGY PHYSICS
, pp. 0–0, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35564.