  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.
