Lorentzian Einstein-Ricci Flows

TL;DR

This paper investigates the Lorentzian Ricci flow within Einstein gravity, demonstrating it as a fixed point of the flow and deriving related renormalization group equations, with linearized analysis revealing heat-like curvature evolution.

Contribution

It introduces the Lorentzian Einstein-Ricci flow, showing Einstein gravity as a fixed point and deriving a novel renormalization group flow in Euclidean signature.

Findings

Einstein gravity is a fixed point of the Lorentzian Ricci flow.

Curvature deformations obey a heat equation with stress-energy as source.

Derived a renormalization group flow in Euclidean signature.

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.