Lorentzian Einstein-Ricci Flows
arXiv:1807.02731
Abstract
We study the Ricci flow for the Lorentzian Einstein-Hilbert action. We show that Einstein gravity emerges as a fixed point of the Einstein-Ricci flow equations and derive a renormalization group flow in Euclidean signature. By considering linearizations near the fixed point, the dynamics of the metric reveal that curvature deformations flow according to a forward heat equation with the stress-energy tensor acting as a source.
4 pages, comments are welcome. v2: Latex, 0 figures; revised argument concerning the RG flow and updated the argument for the geometric flow as a gradient flow; incorporated comments from Jiaping Wang; typos corrected and several minor changes; references added; footnote added